Write $\cos(x)$ in terms of $\sin(x)$ Write $\cos(x)$ in terms of $\sin(x)$ if the terminal point $x$ is in quadrant IV.

I know $\cos^2(x)$ $= 1-\sin^2(x)$. And I know that cos is positive in quadrant IV. I am 

guessing that the answer is $\sqrt{1-\sin^2(x)}$  Can anyone help verify this answer?

Thank you!!
As written, it's not quite correct. Let's start with the identity

$$\sin^2{x} + \cos^2{x} = 1 \implies \cos^2{x} = 1 - \sin^2{x}$$

In quadrant IV, $\cos{x}$ is positive, so taking a square root gives us

$$\cos{x} = \sqrt{1 - \sin^2{x}}$$
$\cos x = 1 - 2 * \sin^2(x/2)$
prove:
\begin{align}
&amp;=&gt;1 - 2 * \sin^2(x/2) \\   
&amp;= 1 - 2 * \sin(x/2) * \sin(x/2)  \\ 
&amp;= 1 - 2 * \sqrt{((1-\cos x)/2)} * \sqrt{((1-\cos x)/2)} \quad \text{NOT: even sqrts are (-), (-)*(-)=(+)}  \\
&amp;= 1 - 2 * (1-\cos x)/2 \\
&amp;= 1 - 1 + \cos x  \\
&amp;= \cos x \\
\end{align}