PERBANDINGAN TRIGONOMETRI (PART 1) SINUS, COSINUS, TANGEN, SECAN, COSECAN, COTANGEN

Summary

This video tutorial provides a comprehensive explanation of basic trigonometric ratios, focusing on sine, cosine, and tangent, as well as their reciprocal functions: cosecant, secant, and cotangent. The video uses a right-angled triangle to illustrate the relationships between the sides and angles, with simple formulas for each ratio. It also guides viewers through step-by-step examples to calculate the ratios and understand their applications. The tutorial further covers how to handle trigonometric problems involving known values and unknown sides, making trigonometry accessible for beginners.

Takeaways

• 😀 The video explains the basics of trigonometric ratios in a right-angled triangle, focusing on sine, cosine, and tangent.
• 😀 Sine (sin), cosine (cos), and tangent (tan) are the primary trigonometric ratios derived from the sides of a right-angled triangle.
• 😀 The sine of an angle is the ratio of the opposite side to the hypotenuse (sin = opposite/hypotenuse).
• 😀 The cosine of an angle is the ratio of the adjacent side to the hypotenuse (cos = adjacent/hypotenuse).
• 😀 The tangent of an angle is the ratio of the opposite side to the adjacent side (tan = opposite/adjacent).
• 😀 The video introduces the reciprocal trigonometric ratios: cosecant (csc), secant (sec), and cotangent (cot).
• 😀 Cosecant is the reciprocal of sine (csc = 1/sin), secant is the reciprocal of cosine (sec = 1/cos), and cotangent is the reciprocal of tangent (cot = 1/tan).
• 😀 A mnemonic is provided to help remember the reciprocal ratios: 'C' (cosecant) is the opposite of 'S' (sine), 'S' (secant) is the opposite of 'C' (cosine), and 'T' (cotangent) is the opposite of 'T' (tangent).
• 😀 To solve for the trigonometric ratios in a triangle, the Pythagorean theorem is applied when the hypotenuse is unknown.
• 😀 Several examples are provided to practice trigonometric ratios, including solving for the missing sides of a triangle and using known ratios to find other trigonometric values.

Q & A

What are the three main trigonometric ratios in a right triangle?

The three main trigonometric ratios in a right triangle are sine (sin), cosine (cos), and tangent (tan).

How is the sine of an angle in a right triangle defined?

The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.

What is the formula for cosine in a right triangle?

The formula for cosine is the ratio of the length of the adjacent side to the length of the hypotenuse.

How can tangent be defined in terms of sine and cosine?

Tangent is the ratio of sine to cosine, or more specifically, the ratio of the opposite side to the adjacent side in a right triangle.

What are the three derived trigonometric ratios, and how are they related to the primary ratios?

The three derived ratios are cosecant (csc), secant (sec), and cotangent (cot). Cosecant is the reciprocal of sine, secant is the reciprocal of cosine, and cotangent is the reciprocal of tangent.

What mnemonic is suggested to help remember the reciprocal relationships of trigonometric functions?

The mnemonic 'C is the opposite of S' is used to remember that cosecant (csc) is the reciprocal of sine (sin), secant (sec) is the reciprocal of cosine (cos), and cotangent (cot) is the reciprocal of tangent (tan).

How is the length of the hypotenuse (AC) calculated in a right triangle when the lengths of the other two sides are known?

The length of the hypotenuse (AC) can be calculated using the Pythagorean theorem: AC = √(AB² + BC²), where AB and BC are the lengths of the other two sides of the right triangle.

What is the significance of the angle alpha (α) in the given triangle?

Angle alpha (α) is used to define the primary trigonometric ratios. The side opposite alpha is used to define sine, the adjacent side to define cosine, and the ratio of these sides is used to define tangent.

How do you find the value of cosine when the length of the sides of a triangle are known?

To find the value of cosine, divide the length of the side adjacent to the angle (AB) by the length of the hypotenuse (AC).

In a triangle with known sine value (e.g., sin(α) = 2/5), how would you find the other trigonometric ratios?

If sin(α) = 2/5, you can construct a right triangle with the opposite side as 2 and the hypotenuse as 5. Then, use the Pythagorean theorem to find the adjacent side. From there, calculate cosine, tangent, secant, cosecant, and cotangent using their respective definitions and relationships.