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)=(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((5)/(13)\right)^2=1-2\left((25)/(169)\right)=1-\left((50)/(169)\right)=(119)/(169)`

The answer is 119/169.