Question

Let sintheta =2times square root 3/5 and pi/2

Answer 1

Given:

$sin\theta=\frac{2\sqrt{3}}{5},\text{ and }\frac{\pi}{2}<\theta<\pi$

It's required to find cos 2θ.

We use the formula:

$cos(2\theta)=1-2sin^2\theta$

Substituting:

$cos(2\theta)=1-2(\frac{2\sqrt{3}}{5})^2$

Operating:

$\begin{gathered} cos(2\theta)=1-2*\frac{4*3}{25} \\ cos(2\theta)=1-\frac{24}{25} \\ cos(2\theta)=\frac{1}{25} \end{gathered}$

Answer: 1/25