Question

Find the value of cos(2x) if sin(x) = 5/13 and x is in Quadrant II.

Answer 1

The given equation is:

$\sin(x)=\frac{5}{13}$

It is required to find the value of cos(2x) if x is in the second quadrant.

Recall the identity:

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

Substitute sin(x)=5/13 into the identity:

$\cos(2x)=1-2\left(\frac{5}{13}\right)^2=1-2\left(\frac{25}{169}\right)=1-\left(\frac{50}{169}\right)=\frac{119}{169}$

The answer is 119/169.