4g Example 2 (Evaluate the Composition of Inverse Trig Functions)

The video tutorial covers the composition of functions, focusing on trigonometric and inverse trigonometric functions. It begins with an introduction to function composition, followed by detailed steps to evaluate compositions without a calculator. The tutorial includes examples of trigonometric function compositions and discusses the importance of understanding inverse functions and their restrictions. The video concludes with a look at reciprocal functions and emphasizes the significance of domain and range restrictions in trigonometric functions.

What is the result of composing the functions F(x) = x^2 and G(x) = 3x - 1?

• 3x^2 - 1

• x^2 + 3x - 1

• 3(x^2 - 1)

• x^2 - 3x + 1

When evaluating the composition of trigonometric functions, what is the recommended approach?

• Use a calculator for accuracy

• Work from the outside in

• Work from the inside out

• Evaluate both functions separately

In which quadrant is the angle located if the sine inverse of a value is negative?

• Third quadrant

• Second quadrant

• First quadrant

• Fourth quadrant

What is the cosine inverse of -sqrt(2)/2?

• 5π/4

• 3π/4

• 7π/4

• π/4

Why is it important to consider restrictions when dealing with inverse trigonometric functions?

• To avoid undefined values

• To ensure the function is continuous

• To simplify calculations

• To stay within the correct range

What is the sine inverse of -1/2?

• -π/6

• π/6

• -π/3

• π/3

Which of the following is a reciprocal trigonometric function?

• Tangent

• Secant

• Cosine

• Sine

What is the cosecant of -π/4?

• -sqrt(2)

• 2/sqrt(2)

• sqrt(2)

• -2/sqrt(2)

How do you find the secant of an angle?

• 1 divided by cotangent

• 1 divided by sine

• 1 divided by cosine

• 1 divided by tangent

What is the cotangent of π/2?

• Undefined

• 1

• 0

• Infinity