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 tangent is using the inverse tangent function and then find the sine of that angle. Since the domain of the inverse tangent function is and the range of is , we will work within this range to solve the problem.

 

Key Concept Explanation

1. The inverse tangent function, or , gives the angle such that and <<.

2. Once we find the angle from , we use the sine 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 hypotenuse and then calculate .

 

Step - by - Step Solution

1. Let

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