SOHCAHTOA using the TI-84 Plus

Summary

This tutorial introduces right triangle trigonometry, focusing on SOA (Sine, Cosine, Tangent) and TOA (Tangent). Mr. Bourne, a math teacher from Minnesota, explains how to use trigonometric ratios to solve problems involving right triangles. He covers setting a calculator to degrees mode, understanding triangle side relationships (opposite, adjacent, hypotenuse), and emphasizes the importance of recognizing right triangles for these methods. The tutorial is part one of a four-part series, promising further examples in subsequent episodes.

Takeaways

• 📚 This tutorial covers SOA TOA, a mnemonic for right triangle trigonometry.
• 👨‍🏫 Mr. Bourne, a math teacher from Minnesota, introduces the concept and its applications.
• 🔢 SOA stands for Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, and Tangent = Opposite/Adjacent.
• 📐 The tutorial helps solve problems involving angles and sides of right triangles.
• 🛠️ It's crucial to set your calculator to degrees mode for these calculations.
• 📈 The tutorial will cover examples of using sine, cosine, and tangent functions.
• 🌐 Greek letters like Theta are sometimes used to represent angles, but they don't change the difficulty.
• 🚫 This method is only applicable to right triangles, not other types of triangles.
• 📉 The tutorial will show how to find angle measures given side lengths or how to find unknown sides given an angle measure.
• 🔄 The hypotenuse is always the longest side opposite the right angle, while opposite and adjacent sides change based on the angle in question.
• 📚 The tutorial is divided into four episodes, each focusing on different aspects of SOA TOA.

Q & A

What does SOA TOA stand for in trigonometry?

SOA TOA is a mnemonic for remembering the trigonometric ratios in a right triangle. SOA stands for Sine, Opposite over Adjacent, and TOA stands for Tangent, Opposite over Adjacent.

What kind of problems can SOA TOA help solve?

SOA TOA can help solve problems where you are given one side length and an angle of a right triangle and need to find another side length, or where you are given two side lengths and need to find an angle measure.

How do you set a calculator to degrees mode for trigonometry problems?

For a TI-83 Plus or TI-84 Plus calculator, press the 'MODE' key, navigate to the third line down where it says 'Radian' and 'Degree', use the right arrow key to highlight 'Degree', and then press 'ENTER' to set the calculator to degrees mode.

What is the significance of the hypotenuse in a right triangle?

The hypotenuse is the longest side of a right triangle and is always opposite the right angle. It remains constant relative to the position of the angle being considered.

What is meant by the term 'adjacent' in the context of a right triangle?

In a right triangle, the 'adjacent' side is the one that is next to the angle being considered and is not the hypotenuse.

How can you verify if your calculator is in degrees mode?

You can verify if your calculator is in degrees mode by typing 'sin(90)'. If the calculator is in degrees mode, it should return 1.

Why is it important to know the difference between 'opposite' and 'adjacent' sides?

Knowing the difference between 'opposite' and 'adjacent' sides is crucial for correctly applying trigonometric ratios like sine, cosine, and tangent to solve for unknown angles or side lengths in a right triangle.

What is the role of the mnemonic SOA TOA in solving trigonometry problems?

The mnemonic SOA TOA helps in remembering the correct placement of sides relative to an angle in a right triangle when applying trigonometric functions, which is essential for solving problems involving unknown angles or sides.

Why might Greek letters be used in trigonometry problems?

Greek letters like Theta (θ) might be used in trigonometry problems to represent unknown angles. This is a way to generalize the problem and does not make the problem more difficult, just a different way of referring to the angle.

What does the acronym SOA represent in the context of the sine function?

In the context of the sine function, SOA stands for Sine, Opposite over Adjacent, which means the sine of an angle in a right triangle is equal to the ratio of the length of the side opposite the angle to the length of the hypotenuse.

How does the position of the angle affect the identification of 'opposite' and 'adjacent' sides?

The position of the angle affects the identification of 'opposite' and 'adjacent' sides because these terms are relative to the angle being considered. The 'opposite' side is always the furthest from the angle, and the 'adjacent' side is the one next to the angle but not the hypotenuse.

Outlines

00:00

📚 Introduction to SOA TOA

This paragraph introduces the tutorial on SOA TOA, also known as right triangle trigonometry. The speaker, Mr. Bourne, a math teacher from Minnesota, explains that this is the first of four episodes. The purpose of the tutorial is to explain what SOA TOA is and the types of problems it can solve. The acronym SOA stands for Sine (opposite/hypotenuse), Cosine (adjacent/hypotenuse), and Tangent (opposite/adjacent), which are ratios used in right triangle trigonometry. Mr. Bourne emphasizes that understanding the relationships between the sides of a triangle and the angles is crucial. He also reassures viewers not to be intimidated by symbols or Greek letters used in some problems. The tutorial is specifically for right triangles, and he clarifies that SOA TOA does not apply to other types of triangles.

05:02

🔍 Applications of SOA TOA

In this paragraph, the speaker discusses practical applications of SOA TOA. It can be used to find the measure of an angle when the lengths of the sides of a right triangle are known. Conversely, if the angle measure and one side length are known, SOA TOA can be used to find an unknown side length. The speaker then provides instructions for setting a TI-83 Plus or TI-84 Plus calculator to degrees mode, which is necessary for these calculations. The process involves accessing the mode menu, selecting 'degree' instead of 'radian', and testing the setting by inputting 'sin 90'. The speaker also explains the importance of identifying the hypotenuse, opposite, and adjacent sides of a triangle in relation to a given angle.

10:05

📐 Understanding Opposite and Adjacent Sides

The final paragraph further clarifies the concepts of opposite and adjacent sides in a right triangle. The speaker uses visual examples to show that these sides can change depending on which angle is being considered. The hypotenuse remains constant as the longest side opposite the right angle. The adjacent side is the one next to the angle, not the hypotenuse, and the opposite side is the one farthest from the angle in question. The speaker emphasizes that understanding these relationships is key to solving problems using SOA TOA. The paragraph concludes with a prompt to watch the subsequent episodes for examples of using sine, cosine, and tangent functions.

Keywords

💡SOA

SOA is a mnemonic used in trigonometry to remember the ratios of sides in a right triangle. It stands for Sine, Opposite, Adjacent. In the context of the video, SOA helps to recall that the sine of an angle (sin) is calculated as the ratio of the length of the side opposite the angle to the length of the hypotenuse. The video uses SOA to introduce the concept of right triangle trigonometry and to solve problems involving the sides and angles of a right triangle.

💡TOA

TOA is another mnemonic used to remember trigonometric ratios, standing for Tangent, Opposite, Adjacent. It refers to the tangent of an angle (tan) being the ratio of the length of the side opposite the angle to the length of the adjacent side. The video explains TOA as part of the introduction to trigonometric functions, emphasizing its use in right triangle trigonometry.

💡Hypotenuse

The hypotenuse is the longest side of a right triangle, opposite the right angle. In the video, the hypotenuse is described as a constant feature in right triangles and is used as a reference for calculating trigonometric ratios. It is highlighted as an essential part of the SOA and TOA mnemonics.

💡Adjacent

Adjacent in trigonometry refers to the side of a right triangle that is next to a given angle, but not the hypotenuse. The video explains that the adjacent side is used in the calculations of both sine and cosine ratios. It is crucial for understanding how to apply the SOA and TOA mnemonics correctly.

💡Opposite

Opposite, in the context of the video, refers to the side of a right triangle that is across from a given angle, not sharing a common vertex. It plays a key role in the definitions of sine and tangent, as it is the numerator in both SOA and TOA mnemonics. The video uses the term to teach how to identify the sides needed for trigonometric calculations.

💡Trigonometry

Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. The video focuses on right triangle trigonometry, specifically using SOA and TOA to solve problems involving the sides and angles of right triangles.

💡Mnemonic

A mnemonic is a memory aid or tool, often in the form of a口诀 or acronym, used to help remember complex information. In the video, SOA and TOA are introduced as mnemonics to help remember the ratios for sine, cosine, and tangent in right triangle trigonometry.

💡Calculator Mode

Calculator mode refers to the setting on a scientific calculator that determines whether angles are measured in degrees or radians. The video provides instructions on setting a TI-84 Plus calculator to degree mode, which is necessary for performing trigonometric calculations as discussed in the tutorial.

💡Radians

Radians are a unit of angular measure used in mathematics, often on calculators. The video mentions that the default setting on some calculators is radian mode, but for the purposes of the tutorial, degree mode is required. Radians are contrasted with degrees to emphasize the importance of using the correct unit for trigonometric calculations.

💡Right Triangle

A right triangle is a triangle with one angle measuring 90 degrees. The video focuses exclusively on right triangles, as the SOA and TOA mnemonics are only applicable to this type of triangle. The concept is fundamental to the tutorial, as it sets the stage for discussing trigonometric ratios.

💡Inverse Functions

Inverse functions are mathematical functions that 'reverse' the effect of the original function. In the context of the video, inverse trigonometric functions like arcsine, arccosine, and arctangent are mentioned as tools for finding angles when the sides of a right triangle are known.

Highlights

Introduction to SOA TOA, a mnemonic for right triangle trigonometry.

SOA stands for Sine, Opposite over Adjacent.

TOA stands for Tangent, Opposite over Adjacent.

SOA TOA is used for solving problems related to right triangles.

How to set a calculator to degrees mode for trigonometry problems.

Verification test for the calculator's degree mode using sin 90.

Explanation of the terms 'opposite', 'adjacent', and 'hypotenuse' in a right triangle.

The importance of knowing the relationship of sides to an angle in a triangle.

The limitations of SOA TOA to right triangles only.

How to identify the hypotenuse in a right triangle.

How to determine the opposite and adjacent sides relative to a given angle.

The significance of the angle's position in identifying triangle sides.

The difference between using Greek letters and standard letters to denote triangle vertices.

How to solve problems where side lengths are given and the angle measure is unknown.

How to solve problems where the angle measure and one side are given to find an unknown side.

The process of setting a TI 83 Plus or TI 84 Plus calculator to degrees mode.

The use of SOA TOA mnemonic for finding angles and sides in right triangles.

The tutorial is part of a four-episode series covering SOA TOA and its applications.

Transcripts

hey there everyone this is a tutorial on

SOA TOA or right triangle trigonometry

and how to use it this is uh the first

of four episodes uh in which you'll see

an introduction to SOA TOA and what kind

of problems it solves uh this is Mr

Bourne and I'm a math teacher in

Minnesota okay if you're already good on

the intro of what soaa is and what it

does you can skip on ahead to episode

two three or four in which uh I will do

some examples of how to use the S and

inverse of s cosine inverse of cosine

and tangent and inverse of tangent so

you get the whole shoo

match okay in this particular episode

this is episode one you'll learn what

problems you can solve how to properly

set your calculator to the degrees mode

and verify it with a little

test and uh last you'll learned a little

bit of vocabulary because you got to

know what uh we're talking about before

you um know what it's uh what it is okay

so real quick

soaa it's a pneumonic which is which is

just a fancy word for um a mental little

trick that you can use in your brain to

remember um what goes where um now

here's how it works so is s and it's

spelled kind of like it sounds so and

the O stands for opposite the H is

hypotenuse and this is something that

you use with sign

so here it is the sign of an angle a is

equal to the

opposite

over the hypotenuse I'm abbreviating

here so you got your

opposite and your hypotenuse right here

so that's what so stands

for K is cosine a adjacent over

hypotenuse so you got your cosine of

your angle and that's a ratio of the

adjacent side of a triangle over the

hypotenuse and if you're already feeling

lost don't worry don't worry that you

don't know what adjacent means you'll

see it in just a minute here and last

one is

TOA which is tangent

whoops

tangent of an angle is equal to the

opposite over the

adjacent so opposite adjacent O A

TOA okay now two quick things here

before we uh get started on to uh

answering the question of what kind of

problems can you solve um don't be

intimidated by all of the symbols I mean

here we've got a triangle and it's it's

got you know all these symbols a b and c

it's dressed up like a Christmas tree

there's lots of symbols everywhere but

don't get hung up on that okay what's

important is knowing the relationship of

like what's across from an angle and

knowing which side of a triangle is the

hypotenuse and um knowing what what side

is the adjacent side relative to an

angle

now sometimes um like in European

countries and well I don't know what

other countries but uh they'll use Greek

letters for referring to the vertices of

triangles and they will they'll ask you

a question that's really intimidating

like this like what's the angle Theta

and they'll bring out this o with a

little line in the middle of it and

that's a Greek letter now like I said

don't get hung up in symbols here

because it just because it's Greek

letters it does not make it any easier

or any harder than what it needs to be

it's just a different way of referring

to different pieces of a triangle and if

they say you know find angle X I mean

don't worry about it it's it's just an

unknown they're just asking for you know

something to be put proper in here

proper letter or

number okay so moving on second thing um

this will not work with other kinds of

triangles as in if it's not a right

triangle uh

like that and if like this middle one

that's not a right triangle uh we can't

use this I mean s cosine and tangent

they do work with other kinds of

triangles but we are specifically doing

right triangle trigonometry and that

means that we need to have this little

box symbol someplace in the Triangle at

some point so um that's kind of crucial

you got to have that right

there if it's not a right triangle we're

not doing this soaa

stuff all right so here's the kind of

problems that uh you would use soaa for

for instance if you were given the side

lengths of a triangle like check it out

you know you got 3 cm and 4 cm let's

just say and here's the all important

little symbol meaning it's a right

triangle then uh you can answer

questions like this you can find out

what the angle measure is for this

little you know spot right here

um so that's one of the applications

another application is where you could

be given the angle measure and one of

the sides and you can use this to figure

out an unknown side so that's really

handy all right now how to properly set

your calculator um if you've got a TI 83

Plus or a TI 84 plus you're in luck now

a lot of times

whenever you're going to start on a

problem it's it seems to be set to the

opposite um angle mode as what you need

it to be now for all of these examples

I'm going to be doing these in degrees

and when you get the calculator from the

factory or when it's reset to its

default settings you'll see that uh the

angle measure will be in radians and uh

radians are not going to be what we use

today I mean they're perfectly fine

there's nothing bad about radians but

we're going to be using degrees and when

we get an answer we want to express it

in degrees now if you've got a TI 83

plus like one of these guys right here

your setting screen looks pretty much

identical it's just that uh the the type

face of the the letters is just a little

bit bigger but it's the same

thing okay so here we're going to uh see

how to set your ti84 plus to degrees

mode and to test

it okay so here's the ti84 plus press

the key in the upper part of the keypad

that has the word mode on it one press

of it and you'll be brought up to the

mode screen there's lots of settings

here the third line down has two choices

radian and degree and if it's uh got

radian that's um highlighted here it's

blackened in the back then um press the

right arrow key over once and then press

the enter key in the lower left I'm

sorry the lower right part of your

keypad so that degree is now highlighted

and uh that's all there is to it

pressing the second key followed by the

mode key will exit you out of the mode

and now your mode is degrees now a fast

way to check just to make sure is to

type in s

90 if it's a one it's in degrees mode

and you're good to go

and right there I went super fast and I

changed into radians mode so you know

you're in radians mode if you put in sin

90 and you get this weird decimal here

that means radians so sin 90 equals one

degrees mode and you're good to

go okay so you've got your calculator

all set up and you know what kind of

problems you can do um now with soaa you

need to know a few things about what's

the opposite what's the adjacent and

what the hypotenuse is so let's just

take a triangle like this and let's just

kind of get rid of all these little

symbols here we don't need these that's

cluttering things

up okay now here's my hypotenuse the

hypotenuse is always the

longest uh side or longest edge of a

right triangle and it is always um on

the far side of your right angle so it's

not too difficult to spot there that's

always the hypotenuse it never changes

so here's what does change let's say

that you were told that

um well let's see how should I do it

let's say that you were told that the

angle measure inside this little angle

right there was

53131

de well um figuring this out that's

where the angle is now we have

to determine which triangle sides are

what since this triangle side is right

next to the degree that we're given this

angle that we're given and the

hypotenuse never changes it always is

there this is the adjacent so it's just

to the side now far

opposite of the angle in

question is the opposite side

so you see we're not so concerned with

ABC uh you know naming sides with those

kinds of labels but in relation to what

where the angle is that we're talking

about there's two locations right so if

we're talking about up here and there's

our angle the opposite side is over here

it's opposite the furthest from and the

adjacent is the triangle leg that is

right next to it that's not the

hypotenuse okay now this one might be a

little bit weird but check this out

let's put these

back and get rid of that thing okay now

suppose just suppose that down here we

were given an angle measure so that's

our angle that we're given now the

opposite is this guy and our adjacent

side is

here adjacent is right next to the angle

measure and it's not the one that's

right next to it that's the hypotenuse

the opposite side of the triangle is the

furthest from the angle opposite side so

now you know what opposite and adjacent

and hypotenuse are in a right triangle

so it can it can change depending on

which of the two unknown angles we're

talking

about all right well that's the end of

episode one uh pick up episode two and

view it to see some examples of sign

episode three to see some examples of

cosine and episode 4 to see some

examples of tangent