How do you find the values of ##sin 2theta## and ##cos 2theta## when ##cos theta = 12/13##?

Get first the value of the of the opposite side fo get ##sin## and use the Double Angle Formula.

##costheta = 12/13## ##c^2=a^2+b^2## ##13^2=a^2 + 12^2## ##a^2=13^2-12^2= 169-144= 25## ##c= sqrt25 =5##

##sintheta = 5/13##

##sin2theta = 2sinu cosu =2(5/13)(12/13)= 120/169##

##cos2theta=cos^2u - sin^2u = (12/13)^2 - (5/13)^2= (144/169) - (5/169)= (144 - 25)/169 = 119/169##