Evaluating the composition of inverse functions trigonometry

The video tutorial explains how to evaluate the inverse sine function, focusing on the correct range for evaluation. It discusses the sine of 2X, emphasizing the relationship between the opposite side and hypotenuse. The tutorial guides viewers through determining the sides of a triangle, ensuring the cosine remains positive. It includes solving for the adjacent side using equations and concludes with finding the cosine and the final answer.

What is the range for evaluating the inverse sine function?

• 0 to π

• -π to π

• 0 to 2π

• -π/2 to π/2

In which quadrants should the triangle be evaluated for the inverse sine function?

• 1st and 2nd

• 2nd and 3rd

• 3rd and 4th

• 4th and 1st

What does the sine of an angle represent in a triangle?

• Hypotenuse over opposite

• Adjacent over opposite

• Opposite over hypotenuse

• Adjacent over hypotenuse

Why must the cosine be positive when evaluating the triangle?

• To ensure the sine is negative

• To simplify the calculation

• To stay within the function's range

• To make the hypotenuse longer

What is the final expression for the cosine of the angle in terms of X?

• sqrt(1 + 4X^2)

• sqrt(1 - 4X^2)

• 4X^2 - 1

• 1 - 4X^2