Geometry

Question Analysis

The main focus is on evaluating the composition of the tangent function and the inverse cosine function. Given , we first find the angle whose cosine is , and then calculate the tangent of that angle. Since the domain of is with , and its range is , we'll work within this range to solve the problem.

 

Key Concept Explanation

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

2. To find for the angle obtained from , we can use the right - triangle relationships. If , we can find the opposite side using the Pythagorean theorem , and then .

 

Step - by - Step Solution

1. Let , so .

Assume a right - triangle where the adjacent side to the angle is

Click "Show Answer" to reveal the answer and analysis