# Given \sin \theta = \frac{5}{2} \text{ and } 0 \theta \frac{\pi}{2}. Find \cos \frac{\theta}{2}

## Question:

Given {eq}\sin \theta = \frac{5}{2} \text{ and } 0 < \theta < \frac{\pi}{2}. {/eq} Find {eq}\cos \frac{\theta}{2} {/eq}

## Trigonometric Functions:

The given value of the cosine theta and the sine theta is to be examined first in order to get the value of the other trigonometric ratios. If this value is greater than 1, then the solution is not possible.

## Answer and Explanation:

We are given {eq}\sin \theta = \frac{5}{2} \text{ and } 0 < \theta < \frac{\pi}{2}. {/eq} we have to find {eq}\cos \frac{\theta}{2} {/eq}

But

{eq}\sin \theta {/eq} can never be greater than 1. So no solution.