How do you find sin2 theta? Where theta is in the fourth quadrant.

sin2theta if costheta=12/13

2 Answers
Feb 18, 2018

sin2θ= -120/169

Explanation:

Given: cosθ=12/13
Therefore draw a triangle in the fourth quadrant and sinθ= -5/13

sin2θ= 2sinθcosθ

sin2θ= 2(-5/13)(12/13)

sin2θ= -120/169

Feb 18, 2018

sin2theta=-120/169

Explanation:

costheta=12/13

costheta="(adj. side)/(hyp)

"Comparing"

"adj. side=12, hyp=13"

"By pythagoras theorem, "

"opp=sqrt(hyp^2-adh^2)=sqrt(13^2-12^2)=5

sintheta="(opp. side)/(hyp)=5/13

sintheta " is negative in fourth quadrant"

sintheta=-5/13

sin2theta=2sinthetacostheta=2xx12/13xx(-5/13)=-120/169

sin2theta=-120/169