Geometry

Question Analysis

The main focus of this problem is to evaluate a composition of trigonometric and inverse trigonometric functions. We first need to find the angle whose sine is  using the inverse sine function and then find the cosine of that angle. Since the domain of the inverse sine function is  and , and we know that the range of  is  in degrees, we will work within this range to solve the problem.

 

Key Concept Explanation

1. The inverse sine function,  or , gives the angle  such that  and  in degrees.

2. Once we find the angle  from , we use the cosine function  to find the value of . The cosine function for an angle  in a right triangle is defined as .

 

Step - by - Step Solution

1. First, find the value of :

We know that  and  is in the range . So,

Click "Show Answer" to reveal the answer and analysis