Question

Find the exact value of sin space 2 theta when tan theta equals negative 12 over 5 where fraction numerator 3 pi over denominator 2 end fraction less or equal than theta less or equal than 2 straight pi.

Answer 1

-120/169

Explanation:

Sin2theta = 2sintheta costheta

Given that tan theta = -12/5

Opposite = -12

Adjacent = 5

Using Pythagoras theorem

Hyp = √(-12)²+5²

Hyp = √144+25

Hyp = √169

Hyp = 13

Cos theta = adj/hyp

Cos theta = 5/13

Sin theta = opp/hyp

Sin theta = -12/13

Substitute

Sin2theta = 2(-12/13)(5/13)

Sin2theta = -120/169

Hence sin 2theta = -120/169