# Math Help - Double Angle Help

1. ## Double Angle Help

Can someone walk me through the following problem:

Find sin2(x) , cos2(x), and tan2(x) if cos(x) = -3/[(13)^(1/2)] and x terminates in quadrant II

Thank You.

2. Originally Posted by super
Can someone walk me through the following problem:

Find sin2(x) , cos2(x), and tan2(x) if cos(x) = -3/[(13)^(1/2)] and x terminates in quadrant II

Thank You.
Hi super,

Since $\cos X = \frac{-3}{\sqrt{13}}$, this means that $x = -3$ and $r=\sqrt{13}$.

Using $r^2=x^2+y^2$, you can determine that $y=2$.

This would make $\sin X = \frac{2}{\sqrt{13}}$

Note that $\sin 2X = 2\sin X \cos X$

Substituting, we arrive at $\sin 2X=2\left(\frac{2}{\sqrt{13}}\right)\left(\frac{-3}{\sqrt{13}}\right)=-\frac{12}{13}$.

Use the double angle identities for $\cos 2X$ and $\tan 2X$ to complete your assignment.