Question

Find sin 2x, cos 2x, and tan 2x, if cosx= -2/sqrt13 and x terminates in quadrant 2 ...?

Answer 1

`cos(x)=- (2)/( √(13) ) \\ \\ \cos^2{x}=(- (2)/( √(13) ) )^2= (4)/(13) \\ \\ \sin^2{x}=1-\cos^2{x}=1-(4)/(13) =(9)/(13) \\ \\ sin(x)= \sqrt{(9)/(13) } = (3)/( √(13) ) \\ \\ sin(2x)=2sin(x)cos(x)=2(3)/( √(13) )(- (2)/( √(13) ) )=- (12)/(13) \\ \\ cos(2x)=\cos^2{x}-\sin^2{x}=(4)/(13) -(9)/(13) =-(5)/(13) \\ \\ tan(2x)= (sin(2x))/(\cos2x)}= (- (12)/(13) )/(-(5)/(13) ) =(12)/(5)`