How to evaluate for the composition of two trigonometric functions

The video tutorial addresses common misconceptions about the cosine inverse function, emphasizing the importance of following the order of operations and understanding restrictions. It explains the concept of reference angles and their role in determining cosine values in different quadrants. The tutorial also guides students on how to identify the correct angle by considering restrictions, using examples like π/4 and 7π/4. The importance of understanding restrictions in trigonometric functions is highlighted to ensure accurate problem-solving.

What is a common mistake students make when dealing with the composition of cosine and inverse cosine?

• Applying the Pythagorean theorem

• Ignoring the unit circle

• Using the sine function instead

• Assuming they always cancel each other out

Why is it important to find the reference angle when working with trigonometric functions?

• It helps in determining the hypotenuse

• It simplifies finding the cosine value

• It is necessary for solving quadratic equations

• It provides the exact value of sine

Which of the following is true about the cosine of π/4?

• It is equal to 1

• It is equal to 0

• It is equal to sqrt(2)/2

• It is equal to -1

How many angles can produce the same cosine value of sqrt(2)/2?

• Three

• Four

• One

• Two

What is the correct angle that produces the cosine value of sqrt(2)/2 within the restricted domain?

• 7π/4

• π/4

• 5π/4

• 3π/4

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

• To ensure the function remains a valid function

• To avoid using the unit circle

• To simplify calculations

• To increase the number of possible solutions

What is the restricted domain for the inverse cosine function?

• π/2 to 3π/2

• 0 to 2π

• π to 2π

• 0 to π