SOLUTION: Use the sum or difference identities to find the exact value of sin -165 degrees

Question 840719: Use the sum or difference identities to find the exact value of sin -165 degrees
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Use the sum or difference identities to find the exact value of sin -165 degrees
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Identity: sin(x-y)=sinxcosy-cosxsiny
sin(-165˚)=sin(60-225)=sin(60)cos(225)-cos(60)sin(225)
..
sin(60)=√3/2
sin(225)=-√2/2(ref angle of π/4 in quadrant III)
cos(60)=1/2
cos(225)=-√2/2(ref angle of π/4 in quadrant III)
..
sin(-165˚)=√3/2*-√2/2-1/2*-√2/2=√6/4-√2/4=(√6-√2)/4
...
Calculator check:
sin(-165˚)=-sin(π/4)≈-0.2588
exact value as calculated: (√6-√2)/4≈-0.2588
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