Question 868399: I'm really stuck on this, any help is greatly appreciated!
Find the exact values of the sine, cosine, and tangent of theta = -(7pi/12)
Thanks again :)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find the exact values of the sine, cosine, and tangent of theta = -(7pi/12)
theta=-(7π/12)=(5π/12)=(2π/12+3π/12)=(π/6+π/4) (reference angle 5π/12 in quadrant III in which sin>0, cos>0, tan>0)
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sin(π/6+π/4)=sin(π/6)*cos(π/4)+cos(π/6)*sin(π/4)=(1/2)*(√2/2)+(√3/2)*(√2/2)=√2/4+√6/4=(√2+√6)/4
cos(π/6+π/4)=cos(π/6)*cos(π/4)-sin(π/6)*sin(π/4)=(√3/2)*(√2/2)-(1/2)*(√2/2)=√6/4-√2/4=(√6-√2)/4
tan(π/6+π/4)=sin(π/6+π/4)/cos(π/6+π/4=(√2+√6)/(√6-√2)
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Calculator check:
tan(-(7π/12))=tan(5π/12)≈3.732… (in quadrant III)
Exact value as calculated=(√2+√6)/(√6-√2)≈3.732…
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sin(-(7π/12))=sin(5π/12)≈-0.9659 (in quadrant III)
Exact value as calculated=-(√2+√6)/4≈-0.9659…
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cos(-(7π/12))=cos(5π/12)≈-0.2588… (in quadrant III)
Exact value as calculated=-(√6-√2)/4≈-0.2588…
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