SOLUTION: find the exact value of sin(1125� + 480�) using sum and difference formulas

Question 797301: find the exact value of sin(1125� + 480�) using sum and difference formulas
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
find the exact value of sin(1125� + 480�) using sum and difference formulas
***
1125=1125-3*360=1125-1080=45deg=reference angle of 45deg in quadrant I
480deg=480-360=120deg=reference angle of 60deg in quadrant II
..
Identity:sin(a+b)=sin(a)cos(b)+cos(a)sin(b)
sin(a)=sin(1125)=sin(45)=√2/2
cos(b)=cos(480)=cos(120)=cos 60(in quadrant II)=-1/2
cos(a)=cos(1125)=cos(45)=√2/2
sin(b)=sin(480)=sin(120)=sin(60)(in quadrant II)=√3/2
..
sin(a+b)=sin(a)cos(b)+cos(a)sin(b)
sin(a+b)=√2/2*(-1/2)+√2/2*√3/2
=-√2/4+√6/4
=(-√2+√6)/4
..
Check:
sin(1125� + 480�)=sin(1605)=sin(165)≈0.2588..
Exact value as calculated=(-√2+√6)/4≈0.2588..

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