Question 802421: find exact values
If sin a=-3/5 and sec b= -5/4, for a fourth quadrant angle a, and a third quadrant angle b, find sin(a+b)
Not sure where I'm going wrong. I keep coming up with 0, but the answer for the review comes up as 24/25.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! find exact values
If sin a=-3/5 and sec b= -5/4, for a fourth quadrant angle a, and a third quadrant angle b, find sin(a+b)
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You are working with 3-4-5 reference right triangles in given quadrants III and IV.
In quadrant III, sin<0, and cos<0.
In quadrant IV, sin<0, and cos>0.
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sin(a+b)=sin(a)cos(b)+cos(a)sin(b)
sin(a)=-3/5 (given)
cos(a)= 4/5
sin(b)=-3/5
cos(b)=-4/5
sin(a+b)=(-3/5*-4/5)+(4/5*-3/5)=(12/25)-(12/25)=0
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Check:
sin(a)=-3/5 in quadrant IV
a≈323.13˚
cos(b)=-4/5 in quadrant III
b≈216.87˚
a+b=323.13+216.87=540˚
sin(a+b)=sin(540˚)=0
Exact answer as calculated=0
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Looks like I got the same answer you did.
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