Geometry

Question Analysis

The main focus of this problem is to evaluate the composition of a trigonometric function () and an inverse trigonometric function (). 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 the range of is , 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 .

2. Once we find the angle from , we use the cosine function to find the value of . In a right triangle, if , we can use the Pythagorean theorem (where is the hypotenuse and and are the legs of the right triangle) to find the length of the other side and then calculate .

 

Step - by - Step Solution

1. Let

Click "Show Answer" to reveal the answer and analysis