Question 995648
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Find sin2x, cos2x, and tan2x if cosx= -15/17 and x terminates in quadrant III.
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sin(x) = {{{sqrt(1 - cos^2(x))}}} = {{{sqrt(1 - (-15/17)^2)}}} = {{{sqrt(1 - (225/289))}}} = {{{sqrt((289-225)/289))}}} = {{{sqrt(64/289)}}} = (-8/17). 


The sign is  "minus"  because the angle is in the quadrant III.


Now,  sin(2x) = 2*sin(x)*cos(x) = {{{2}}}.{{{(-8/17)}}}.{{{(-15/17)}}} = (*)     (calculate yourself).


cos(2x) = {{{sqrt(1-sin^2(2x))}}} = (**)     (calculate yourself using (*)).


tan(2x) = {{{(sin(2x))/(cos(2x))}}} = calculate yourself using (*) and (**).