Trigonometry For Beginners!

Summary

This video script offers an in-depth exploration of right triangle trigonometry, focusing on the SOHCAHTOA mnemonic to understand and calculate the sine, cosine, and tangent of an angle in a right triangle. The lesson explains the relationship between the angle, the sides adjacent to and opposite it, and the hypotenuse. It demonstrates how to find missing sides using the Pythagorean theorem and how to calculate the values of the six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) for given sides of a triangle. The script also covers special right triangles, such as the 3-4-5 triangle, and provides methods to solve for missing angles and sides using trigonometric functions. Additionally, it touches on the application of these concepts in real-world problems and teases an upcoming comprehensive trigonometry course on Udemy, covering topics from angles and the unit circle to trigonometric identities and equations.

Takeaways

• 📐 **SOHCAHTOA**: A mnemonic for right triangle trigonometry, where Sine is Opposite over Hypotenuse, Cosine is Adjacent over Hypotenuse, and Tangent is Opposite over Adjacent.
• 🔢 **Pythagorean Theorem**: Applies to right triangles as \( a^2 + b^2 = c^2 \), where \( c \) is the hypotenuse.
• 🔁 **Reciprocal Functions**: Cosecant is the reciprocal of sine, secant is the reciprocal of cosine, and cotangent is the reciprocal of tangent.
• 🔍 **Finding Missing Sides**: Use the Pythagorean theorem to find the missing side in a right triangle when two sides are known.
• 📈 **Special Triangles**: Memorizing special right triangles like 3-4-5, 5-12-13, 8-15-17, and multiples of these can help quickly find missing sides.
• 📌 **Trigonometric Values**: Calculate the values of sine, cosine, and tangent using the sides of a right triangle relative to an angle.
• 🔮 **Finding Angles**: Use inverse trigonometric functions (arcsin, arccos, arctan) to find the measure of an angle when the ratio of sides is known.
• 🔗 **Related Functions**: Tangent relates the opposite and adjacent sides, while cosine and sine relate to the adjacent/hypotenuse and opposite/hypotenuse, respectively.
• 🧮 **Calculator Usage**: Utilize a calculator in degree mode to find the values of trigonometric functions and their inverses for specific angles.
• 📚 **Trigonometry Course**: The speaker offers a course on Udemy covering various topics from angles and the unit circle to trigonometric identities and applications.
• 📈 **Graphing Trigonometric Functions**: Learn how to graph sine, cosine, secant, cosecant, and tangent functions, as well as understand their properties and applications.

Q & A

What is the expression 'sohcahtoa' used for in trigonometry?

The expression 'sohcahtoa' is a mnemonic for remembering the definitions of the primary trigonometric functions sine, cosine, and tangent in terms of the sides of a right triangle. 'S' stands for sine, 'O' for opposite, 'H' for hypotenuse, 'C' for cosine, 'A' for adjacent, and 'TOA' for tangent.

What are the three sides of a right triangle that are relevant to trigonometry?

The three sides of a right triangle relevant to trigonometry are the opposite side (to the angle theta), the adjacent side (next to the angle theta), and the hypotenuse (the longest side, across from the right angle).

What is the Pythagorean theorem, and how does it apply to right triangles?

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Expressed as an equation, it is a^2 + b^2 = c^2.

How do you find the missing side of a right triangle when given the values of two sides?

To find the missing side of a right triangle when two sides are given, you use the Pythagorean theorem (a^2 + b^2 = c^2). Substitute the known side lengths for 'a' and 'b', solve for 'c', and then take the square root of the result to find the length of the hypotenuse.

What are the reciprocal trigonometric functions, and how are they related to the primary ones?

The reciprocal trigonometric functions are cosecant (csc), secant (sec), and cotangent (cot). Cosecant is the reciprocal of sine (csc θ = 1/sin θ), secant is the reciprocal of cosine (sec θ = 1/cos θ), and cotangent is the reciprocal of tangent (cot θ = 1/tan θ).

What are some special right triangles with whole number side lengths?

Special right triangles with whole number side lengths include the 3-4-5 triangle, the 5-12-13 triangle, the 8-15-17 triangle, and the 7-24-25 triangle. These triangles are derived from the Pythagorean theorem and have side lengths that are multiples of the smallest Pythagorean triple (3, 4, 5).

How do you calculate the values of the six trigonometric functions for a given right triangle?

To calculate the values of the six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) for a given right triangle, you first identify the lengths of the opposite, adjacent, and hypotenuse sides relative to the angle in question. Then, apply the definitions of each trigonometric function using these side lengths.

How can you find the missing side of a right triangle if you know the angle and one side?

If you know one side and an angle in a right triangle, you can find the missing side by using the appropriate trigonometric function related to the known side: sine for the opposite side, cosine for the adjacent side, or tangent for the ratio of the opposite to the adjacent side. Then, apply the Pythagorean theorem to find the hypotenuse if needed.

What is the process to find the angle theta in a right triangle if you are given the lengths of the opposite and adjacent sides?

To find the angle theta when the lengths of the opposite and adjacent sides are known, use the tangent function, which is the ratio of the opposite side to the adjacent side (tan θ = opposite/adjacent). Then, use the inverse tangent function (arctan or tan^(-1)) to find the angle theta.

How do you find the value of an angle in a right triangle if you know the lengths of the hypotenuse and the adjacent side?

To find the value of an angle in a right triangle when the lengths of the hypotenuse and the adjacent side are known, use the cosine function (cos θ = adjacent/hypotenuse). Then, apply the inverse cosine function (arccos or cos^(-1)) to determine the angle.

What is the purpose of the trigonometry course mentioned in the script?

The purpose of the trigonometry course is to provide a comprehensive understanding of trigonometry concepts, including angles, the unit circle, right triangle trigonometry, trigonometric functions, and their applications. The course also covers solving trigonometric equations, verifying trig identities, and using trigonometric functions to solve real-world problems.

Outlines

00:00

📐 Introduction to Right Triangle Trigonometry

This paragraph introduces the concept of right triangle trigonometry, focusing on the SOHCAHTOA mnemonic to remember the relationships between the sides and angles of a right triangle. It explains the terms 'opposite', 'adjacent', and 'hypotenuse' in relation to an angle theta, and how these sides are used in the definitions of the primary trigonometric functions: sine, cosine, and tangent. It also covers the reciprocal functions: cosecant, secant, and cotangent. The Pythagorean theorem is mentioned as a tool to find missing sides. The paragraph concludes with an example of finding the missing side of a triangle with given side lengths and subsequently calculating all six trigonometric functions for that triangle.

05:01

🔢 Applying Trigonometric Functions to Find Missing Sides

This paragraph continues the discussion on right triangle trigonometry by demonstrating how to find missing sides using the Pythagorean theorem and then calculating the values of all six trigonometric functions for a given triangle. It provides a step-by-step example using a triangle with sides of lengths 8 and 17, showing how to determine the missing side and then use SOHCAHTOA to find the values of sine, cosine, tangent, cosecant, secant, and cotangent. The paragraph also mentions special right triangles and their multiples as a quick way to find missing sides without the Pythagorean theorem.

10:02

🧮 Solving Triangles with Given Sides and Calculating Trigonometric Functions

The paragraph presents a method for solving right triangles when the lengths of two sides and one angle are known. It illustrates the process of finding the missing side using the Pythagorean theorem and then applying trigonometric functions to find the values of sine, cosine, and tangent. The reciprocal functions are also calculated by inverting the ratios. The paragraph includes an example with a hypotenuse of 25 and a side of 15, showing that the missing side is 20, and then calculates the trigonometric functions for this specific triangle.

15:03

📐 Using Trigonometric Functions to Find Angles and Sides

This paragraph discusses how to use trigonometric functions to find missing angles and sides in a right triangle. It provides examples of using tangent, cosine, and sine functions to solve for an unknown side when the angle and one side are known. The paragraph demonstrates cross-multiplication and the use of a calculator to find the values of unknown sides for different given angles and side lengths. It emphasizes the importance of setting up the trigonometric equation correctly and using the appropriate function based on the given information.

20:03

📚 Accessing a Comprehensive Trigonometry Course

The final paragraph promotes a comprehensive trigonometry course available on Udemy that covers a wide range of topics in trigonometry. It outlines the course content, which includes angles, radians, the unit circle, right triangle trigonometry, trigonometric functions of any angle, graphs of trigonometric functions, inverse trig functions, composition of trig functions, applications, verifying trig identities, and various trigonometric formulas. The paragraph also mentions that some sections are still being added and provides instructions on how to find and access the course.

🔍 Further Topics and Course Completion

This paragraph mentions additional topics that will be included in the trigonometry course, such as the law of sines, law of cosines, polar coordinates, and others. It notes that about two-thirds of the course has been completed and that more content will be added over time. The paragraph invites students to ask questions and thanks them for watching the video.

Keywords

💡Sohcahtoa

Sohcahtoa is a mnemonic used to remember the definitions of the primary trigonometric functions for acute angles in a right triangle. The acronym stands for 'Sine is Opposite over Hypotenuse, Cosine is Adjacent over Hypotenuse, Tangent is Opposite over Adjacent.' It is central to the video's theme of right triangle trigonometry, helping to relate the angles of a triangle to the lengths of its sides. In the script, it is used to explain how to calculate sine, cosine, and tangent for an angle theta in a right triangle.

💡Right Triangle Trigonometry

Right triangle trigonometry is the study of the relationships between the angles and sides of a right triangle, particularly using the primary trigonometric functions: sine, cosine, and tangent. It is the main theme of the video, which focuses on how to use these relationships to solve for missing side lengths and angles in a right triangle. The script provides several examples of using trigonometric functions to find missing sides and angles in various right triangles.

💡Pythagorean Theorem

The Pythagorean theorem is a fundamental principle in geometry that states in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This theorem is used in the script to find the missing side of a right triangle when the lengths of the other two sides are known, as in the example where sides of lengths 3 and 4 are given to find the hypotenuse.

💡Trigonometric Functions

Trigonometric functions, such as sine, cosine, and tangent, are mathematical functions that describe the relationship between the angles and sides of a right triangle. In the video, these functions are used to solve for missing sides and angles in right triangles. The script explains how to calculate these functions using the sides of a triangle and provides examples of their application in solving trigonometry problems.

💡Special Right Triangles

Special right triangles are right triangles with side lengths that have specific integer ratios, such as 3-4-5 or 5-12-13. These triangles are important in the video because they allow for quick identification of missing sides without the need for complex calculations. The script mentions several special triangles and their multiples, which can be used as shortcuts for finding missing sides in similar triangles.

💡Reciprocal Trigonometric Functions

Reciprocal trigonometric functions, such as cosecant, secant, and cotangent, are the reciprocals of the primary trigonometric functions sine, cosine, and tangent, respectively. They are introduced in the script as a means to find the lengths of sides in a right triangle when given the values of the primary trigonometric functions. For instance, the cosecant is the reciprocal of sine, secant is the reciprocal of cosine, and cotangent is the reciprocal of tangent.

💡Inverse Trigonometric Functions

Inverse trigonometric functions, also known as arc functions, are used to find the measure of an angle from the known values of a trigonometric function. In the video, the inverse functions are used to determine angles when the lengths of the sides of a right triangle are known. For example, the script shows how to use the arc tangent function to find an angle when the tangent of that angle is given.

💡Angle of Elevation and Depression

The angle of elevation and depression are concepts used to describe the angle of sight from an observer's line of sight to an object above or below the horizontal line of sight, respectively. While not explicitly detailed in the script, it is implied as a potential application of right triangle trigonometry when discussing the use of trigonometric functions to solve real-world problems.

💡Unit Circle

The unit circle is a circle with a radius of one unit and is used in the context of the video to define the trigonometric functions for all angles, not just those in right triangles. It is a fundamental concept in trigonometry that extends the application of trigonometric functions to include angles greater than 90 degrees. The script mentions the unit circle in relation to the six trigonometric functions and their definitions.

💡Trigonometric Identities

Trigonometric identities are equations that hold true for all values of the variables involved and are used to simplify and manipulate trigonometric expressions. The script briefly mentions verifying trig identities as a challenging aspect of trigonometry, which involves proving that two trigonometric expressions are equivalent using properties and relationships of the trigonometric functions.

💡Trigonometry Course

The script concludes with a reference to a trigonometry course available on the Udemy platform. The course is designed to cover various aspects of trigonometry, including angles, the unit circle, right triangle trigonometry, and applications of trigonometric functions. The mention of the course serves as a resource for viewers who wish to deepen their understanding of the subject matter presented in the video.

Highlights

The expression 'sohcahtoa' is introduced as a mnemonic for the sine, cosine, and tangent ratios in right triangle trigonometry.

The sides of a right triangle are defined as opposite, adjacent, and hypotenuse relative to an angle theta.

The Pythagorean theorem is mentioned in the context of right triangles, stated as a squared plus b squared equals c squared.

Six trigonometric functions are explained using the 'sohcahtoa' mnemonic: sine, cosine, tangent, cosecant, secant, and cotangent.

The process of finding the missing side of a right triangle using the Pythagorean theorem is demonstrated.

Special right triangles with side ratios like 3-4-5 and 5-12-13 are introduced to simplify finding missing sides.

Values of sine, cosine, and tangent for a given right triangle are calculated using the 'sohcahtoa' mnemonic.

The reciprocal trigonometric functions cosecant, secant, and cotangent are derived from their respective primary functions.

An example problem is solved to find the missing side and the values of all six trigonometric functions for a given triangle.

The concept of special triplets for right triangles is used to find missing sides without using the Pythagorean theorem.

The values of the six trigonometric functions are found for a triangle with sides of lengths 8 and 17, using the 'sohcahtoa' mnemonic.

The hypotenuse of a right triangle is calculated when two other sides are known, using the Pythagorean theorem.

Trigonometric function values are calculated for a triangle with a hypotenuse of 25 and a side of 15, illustrating the 'sohcahtoa' mnemonic.

The process of finding the value of an unknown side (x) in a right triangle using tangent is demonstrated with an example.

Calculating the value of x using cosine when the adjacent side and the hypotenuse are known is shown step by step.

An example is provided to find the value of x using sine when the opposite side and the hypotenuse are given.

The method to find the angle theta using tangent when the opposite and adjacent sides are known is explained.

The course curriculum for a comprehensive trigonometry course is outlined, covering topics from angles and the unit circle to trigonometric identities and applications.

Access to the trigonometry course on Udemy is provided for interested learners to deepen their understanding of the subject.

Transcripts

have you ever heard of the expression

sohcahtoa

what do you think this expression means

in this lesson we're going to focus on

right triangle trigonometry

let's say if this is the angle theta

now there's three sides of this triangle

that you need to be familiar with

opposite to theta this is the opposite

side

and next to the angle of theta is the

adjacent side

and across the box or the right angle of

the triangle which is the hypotenuse

that's the longer side of the triangle

now if you recall

this is a b and c the pythagorean

theorem applies to right triangles a

squared plus b squared is equal to c

squared

but we're not going to focus on that too

much but just be familiar with that

equation

now let's talk about the six trig

functions in terms of sine cosine

tangent

opposite adjacent hypotenuse

sine theta

according to sohcahtoa

s is for sine o is for opposite h is for

hypotenuse sine theta is equal to the

opposite side

divided by the hypotenuse

cosine theta

is equal to the adjacent side

divided by the hypotenuse

k

is for cosine is adjacent over

hypotenuse

and tangent theta

toa

is equal to the opposite side divided by

the adjacent side so that's the tangent

ratio it's opposite over adjacent

now we know that cosecant

is one over sine so cosecant is

basically hypotenuse divided by the

opposite side you just need to flip

this particular fraction

secant

is the reciprocal

of cosine so secant is going to be

hypotenuse divided by the adjacent side

cotangent

is the reciprocal of tangent so if

tangent is opposite over adjacent

cotangent is adjacent divided by the

opposite side

now let's say if we're given

a right triangle

and we have the value of two sides let's

say this is three and this is four

and here is the angle theta

find the missing side of this right

triangle

and then

find the values of all six trigonometric

functions sine cosine tangent secant

cosecant cotangent

now to find the missing side

we need to use the pythagorean theorem

a squared plus b squared is equal to c

squared

so a is three b is four

and we gotta find missing side

c

which is the hypotenuse

three squared is nine four squared is

sixteen

nine plus sixteen is 25

and if you take the square root of both

sides

you can see that the hypotenuse is 5.

now it turns out that there are some

special numbers

there's the three four five right

triangle the 5 12 13 right triangle

the 8 15 17 right triangle

and the 7 24 25 right triangle

and any whole number ratios or multiples

of these numbers will also work for

example if we multiply this by 2

we'll get 6 8 10.

that can also work or

if you multiply by 3

you get the 9 12 15 triangle

if you multiply this one by 2 you get

the 10

24 26 triangle

those are also special triplets

they work with any right triangle

now some other numbers that

are less common but you might see

are the 9 40 41 triangle and the 1160

61.

so if you see some of these numbers you

can find the missing side quickly

if you know them

so now let's finish this problem

so what is the value of sine theta

so according to sohcahtoa

we know that sine theta

is equal to the opposite side divided by

the adjacent side

and the part so

soh

opposite to

theta

is

4.

and hypotenuse is five so therefore sine

theta

is going to be four divided by five

now cosine theta

is equal to the adjacent side divided by

the hypotenuse

we said 4 is the opposite side

5 is the hypotenuse and 3 is the

adjacent side so in this case is going

to be 3 divided by 5.

so that's the value of cosine

now let's find the value of tangent

tangent theta according to toa

is equal to the opposite side divided by

the adjacent side

so that's going to be 4 divided by 3

so that's the value of tangent

now once we have these three we can

easily find the other three

to find cosecant

it's one over sine so just flip this

fraction is going to be five over four

and secant is the reciprocal of cosine

so flip this fraction secant is going to

be five over three

cotangent is the reciprocal of tangent

so if cotan i mean if tangent's four

over three cotangent is going to be

three over four and that's how you could

find the value of the six trigonometric

functions

let's try another problem

so let's say this is theta again

and this side is eight and this side is

17.

find the missing side

and then

use the completed triangle to find the

value of the six trigonometric functions

so go ahead and pause the video and work

on this problem

so first we need to know that this is

the 8 15 17 triangle

if you ever forget you can fall back to

this equation

so a is 8 we're looking for the missing

side b and the hypotenuse is 17.

8 squared is 64

and 17 squared is 289

289 minus 64 is 225

and we need to take the square root of

both sides and the square root of 225 is

15

which gives us the missing side of the

triangle

so now go ahead and find the value of

sine theta

cosine theta

tangent theta

and then cosecant theta

secant theta

and cotangent theta

so using sohcahtoa

we know that sine

is equal to the opposite side divided by

the hypotenuse

so let's label all the three sides 17 is

the hypotenuse

8 is the adjacent side

and opposite to theta is 15.

so opposite over hypotenuse this is

going to be 15 divided by 17.

so that is the value

of sine theta now cosine theta

is going to be equal to the adjacent

side

divided by the hypotenuse

so the adjacent side is 8 they have hot

news is 17. so cosine theta

is 8 over 17.

tangent based on toa is going to be

opposite

over adjacent

so opposite is 15 adjacent is 8.

therefore tangent

is going to be 15 divided by eight

now cosecant is the reciprocal of sine

so if sine theta is 15 over 17 cosecant

is going to be 17 over 15.

secant is the reciprocal of cosine so if

cosine is 8 over 17 secant is 17 over 8.

you just got to flip it and cotan is a

reciprocal of tangent

so cotangent is going to be 8 over 15.

just flip this fraction

and now we have the values

of the six trigonometric functions

and that's all you gotta do

so here's a different problem

so let's say here's our right angle and

this time this is theta

and let's say the hypotenuse is 25

and this side is 15.

find the missing side and then go ahead

and find the value of the six

trigonometric functions

so this is going to be similar to the

three four five triangle

notice that if we multiply everything by

five

we'll get two

of the three numbers that we need three

times five is fifteen four times five is

twenty five times five is twenty five

so we have the fifteen

and we have the twenty five

therefore the missing side must be

twenty

and you could use the pythagorean

theorem to confirm this if you want to

so now let's go ahead and find the value

of sine theta

so opposite to theta

is 20.

the hypotenuse is always across the box

it's the longer side

so 27 is the hypotenuse

and adjacent to 15 or right next to it

is 15.

i mean adjacent to theta is 15.

now sine theta we know it's opposite

divided by hypotenuse so it's 20

over 25

which reduces to 4 over 5.

if we divide both numbers by 5. 20

divided by 5 is 4

25 divided by 5 is 5.

cosine theta

is adjacent over hypotenuse so that's 15

divided by 25 which reduces to 3 divided

by 5.

tangent theta

is opposite over adjacent

so 20 over 15

which

becomes

if you divide by 5 that's going to be 4

over 3.

now cosecant is the reciprocal of sine

so it's going to be 5 over 4

based on

this value

and if cosine is 3 over 5

then secant the reciprocal of cosine has

to be 5 divided by 3.

now if tangent

is 4 over 3 cotangent has to be 3

divided by 4.

and so that's it for this problem

consider the right triangle

in this right triangle find

the missing side in this case find the

value of x let's say the angle is 38

degrees

and this side is 42.

so what trig function

should you use in order to find the

value of x

should we use sine cosine or tangent

well relative to 38

we have the opposite side

which is x

and the adjacent side

which is 42.

so tangent we know it's opposite over

adjacent so therefore tangent

of the angle 38 degrees

is equal to the opposite side x

divided by the adjacent side 42

so in order to get x by itself we need

to multiply both sides by 42.

so these will cancel

so therefore x

is equal to 42

tangent of 38

so we need to use the calculator to get

this answer

and make sure your calculator is in

degree mode

so tan 38

which is 0.7813

and let's multiply that by 42

so this will give you an x value of 32.8

now let's try another example

feel free to pause the video to work on

each of these problems by the way

so let's say this angle is 54 degrees

and we're looking for the value of x and

hypotenuse is 26

which trig function should we use sine

cosine of tangent

so opposite to the right angle we know

it's the hypotenuse

and x is on the adjacent side relative

to 54.

so cosine

is associated with adjacent and

hypotenuse

so therefore cosine of the angle 54

is equal to the adjacent side x divided

by

the hypotenuse of 26

so to get x by itself we got to multiply

both sides by 26

so therefore x

is equal to 26

cosine

of 54 degrees

cosine 54

is 0.587785

if we multiply that by 26

this will give us the value of x which

is 15.28

here's another one that we could try

let's say the angle is 32 degrees

and the hypotenuse is x

and this is 12.

so notice that 12 is opposite to

32

and we have the hypotenuse so this time

we need to use the sine function

sine of the angle 32

is equal to the opposite side 12

divided by x

so in this case what can we do to find

the value of x

what would you do

what i would do is cross multiply

so 1 times 12

is 12

and this is going to equal

x times sine 32.

next

i recommend dividing both sides by sine

thirty-two

sine thirty-two divided by itself is one

so therefore x

is equal to 12

over sine 32.

12 divided by sine 32 is 22.64

so that's the value of x in this

particular problem

now let's work on another problem

so this time

we need to find the angle theta

and we're given these two sides

so 5 is opposite to the angle

and 4 is adjacent to it

so what trig function

can relate theta 4 and 5

we know tangent is opposite over

adjacent so tangent of the angle theta

is equal to the opposite side which is 5

divided by the adjacent side 4.

so how can we find the value of the

angle theta

if tangent theta is 5 over 4

and then theta

is going to be the inverse tangent or

arc tangent of 5 over 4 and you simply

have to type this in your calculator

so type in

arc tan 5 over 4

and you should get an angle

of

51.34 degrees

so that's how you could find the missing

angle

let's try another example

feel free to pause the video and find a

missing angle

so in this case we have the adjacent

side

and we have the hypotenuse

so therefore this is associative of

cosine

cosine theta is equal to the adjacent

side

divided by the hypotenuse so if cosine

theta is equal to 3 divided by 7

theta is going to be arc cosine 3 over

7.

and once again you have to use a

calculator to figure this out because

without a calculator out of you know

what this answer is

and this is going to be

64.62 degrees

so here's another one for you

let's say this is 5 and this is 6.

go ahead and find the value of theta

so the hypotenuse is 6

opposites of theta is five

so we know sine is associated with

opposite and hypotenuse

sine theta is equal to the opposite side

which is five

divided by the hypotenuse which is six

therefore theta

is the arc sine or inverse sine of five

over six

and so the angle is going to be

56.44 degrees

and that's it that's all you got to do

to find the missing angle of a right

triangle

for those of you who might be interested

in my trigonometry course

here's how you can access it

so

go to udemy.com

and once you're there

enter into the search box trigonometry

now this is a course i've recently

created so

i haven't finished

adding all the sections that i want to

add so anytime i'm going to do that

right now the page is accessible on the

uh you can find the course on the second

page and here it is trigonometry the

unit circle angles

and right triangles is basically the one

with the dark background

and a circle with a triangle inside the

circle

so let's look at the curriculum in the

first section

i'm going to go over angles

radians how to convert degrees to

radians

coterminal angles

how to convert dms to decimal degrees

arc length

area of the sector of a circle

linear speed and angular speed word

problems and also if you need to take

the time that's shown on the clock and

if you need to convert it to an angle

measure

i cover that in this section as well

and then at the end of each section is

the video quiz

the next section is about the unit

circle the six trig functions

sine cosine tangent secant cosecant

cotan

and also reference angles as well

after that you have right triangle

trigonometry

things like sohcahtoa

the special right triangles like the

30-60-90 triangle

you need to know that so you can

evaluate

sine and cosine

functions

without using the unit circle

next

i'm going to talk about how to solve

angle of elevation and depression

problems

and just solving the missing sides of

right triangles

after that trigonometric functions of

any angle

and then the graph intrigue functions

you need to know how to graph the sine

and cosine

functions secant cosecant

and tangent as well

after that

inverse trig functions you need to know

how to evaluate it

and also how to graph it too

in addition you need to know how to

graph or evaluate composition of trig

functions for example we might have

sine of inverse cosine of 3 over 4 or

something like that and you can use a

right triangle

to solve those types of problems you'll

see when you

access that section after that

applications of trig functions

solving problems to have two right

triangles in it

and

barons as well

one of the hardest actions in trig is

this section verifying trig identities

so that's uh

that's a hard one so make sure you spend

some time

learning that section after that summer

difference formulas

double angle half angle power reducing

formulas

product to sum sum to product

and also solve and trig equations

but there are still some sections i'm

going to add to this course like for

example law of sines law of cosines

polar coordinates and some other topics

as well

so about two-thirds of the course is

finished so far and for most students

this is just what they need intrigued

but in time you'll see more

so now you know how to access the course

and if you have any questions let me

know

so thanks for watching

you