4g Example 3 (Composition of Inverse Trig with right Triangles)

The video tutorial explains how to evaluate trigonometric compositions when values are not on the unit circle. It emphasizes using triangles to understand trigonometric functions like sine, cosine, and tangent. The tutorial covers solving problems using inverse functions and handling negative values. It also explores abstract concepts involving unknowns, using algebraic expressions to represent trigonometric relationships.

Why do we need to revert to basic trigonometric functions when dealing with unfamiliar values on the unit circle?

• Because the unit circle only works for known values.

• Because unfamiliar values are not on the unit circle.

• Because the unit circle is not accurate.

• Because triangles are easier to understand.

What is the sine of an angle if the cosine of the angle is 4/5?

• 5/4

• 1/5

• 4/5

• 3/5

When given sine inverse of 1/3, what trigonometric function are we trying to find?

• Tangent

• Secant

• Cosecant

• Cosine

Why is it important to consider quadrant restrictions when dealing with negative values in trigonometric functions?

• To simplify calculations.

• To correctly evaluate inverse functions.

• To avoid undefined values.

• To ensure the angle is positive.

In which quadrants are the inverse tangent functions restricted?

• First and Second

• Second and Third

• First and Fourth

• Third and Fourth

What is the cosine of an angle if the tangent of the angle is -3/2?

• -2/sqrt(13)

• 3/sqrt(13)

• -3/sqrt(13)

• 2/sqrt(13)

How do we handle unknown variables in trigonometric functions?

• By using the unit circle.

• By creating a triangle and using algebraic expressions.

• By guessing the values.

• By using a calculator.

What is the tangent of an angle if the cosine inverse is given as 1/x?

• x/sqrt(1-x^2)

• sqrt(x^2-1)/x

• sqrt(1-x^2)/x

• 1/sqrt(x^2-1)

What is the sine of an angle if the tangent is x/2?

• 2/x

• x/2

• x/sqrt(2+x^2)

• 2/sqrt(2+x^2)

What should you do if you encounter a trigonometric value not on the unit circle?

• Use a different trigonometric function.

• Ignore the value.

• Revert to understanding of triangles.

• Use a calculator.