SOLUTION: find the sin(a+b) if tan(a) = 7/24 where a is in the third quadrant and cos (b)= -12/13 where b is in the second quadrant

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Question 467644: find the sin(a+b) if tan(a) = 7/24 where a is in the third quadrant and cos (b)= -12/13 where b is in the second quadrant
Answer by lwsshak3(11628) About Me  (Show Source):
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Find the sin(a+b) if tan(a) = 7/24 where a is in the third quadrant and cos (b)= -12/13 where b is in the second quadrant
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Identity required: sin(a+b)=sin a cos b +cos a sin b
so we must find sin a, sin b, cos a and cos b
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Given: tan (a) =7/24 in quadrant III
This gives a hypotenuse=√(24^2+7^2)=√625=25
In quadrant III, both sin and cos are <0
sin a=-7/25
cos a=-24/25
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Given: cos (b)=-12/13 in quadrant II (cos<0, sin>0)
Opposite leg=√(13^2-12^2)=√25=5
Sin b=5/13
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sin(a+b)=(-7/25)(-12/13)+(-24/25)(5/13)
=.2585-.3692=.1107
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ans: sin(a+b)=.1107