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

Question

$sin2theta if costheta=12/13$

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Answer 1 · 2018-02-18T17:39:45

$sin2θ= -120/169$

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

$sin2θ= 2sinθcosθ$

$sin2θ= 2(-5/13)(12/13)$

$sin2θ= -120/169$

Answer 2 · 2018-02-18T17:40:45

$sin2theta=-120/169$

$costheta=12/13$

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

$"Comparing"$

$"adj. side=12, hyp=13"$

$"By pythagoras theorem, "$

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

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

$sintheta " is negative in fourth quadrant"$

$sintheta=-5/13$

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

$sin2theta=-120/169$