Use the given information to find the values of sin 2theta c

Use the given information to find the values of sin 2theta. cos2theta. and tan 2theta. Sin theta = -15/17; The terminal side of theta lies in quadrant III.sin 2theta = (Simplify sour answer, including any radicals. Use integers or fractions for any numbers in the expression) cos2theta = Square (Simplify sour answer, including any radicals. Use integers or fractions for any numbers in the expression) tan 2 theta =Square (Simplify sour answer, including any radicals. Use integers or fractions for any numbers in the expression)

Solution

sin = -15/17 is in QIII

now by sin^2 +cos^2 =1

cos^2 = 1- (-15/17)^2

cos = -8/17

so now sin2 =2sin.cos

= 2(-15/17) .(-8/17)

= 240/289

cos2 =cos^2 -sin^2

= (-8/17)^2 - (-15/17)^2

=64/289 - 225/289

= -161/289

tan(2) = sin2/cos = 240/-161

= -240/161