SOLUTION: If sin p=3/5 and tan q=5/12, find the exact value of sin (p-q). (p and q are acute angles) Thorough steps and details to the answer, please.

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Question 921735: If sin p=3/5 and tan q=5/12, find the exact value of sin (p-q). (p and q are acute angles) Thorough steps and details to the answer, please.
Answer by lwsshak3(11628) About Me  (Show Source):
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If sin p=3/5 and tan q=5/12, find the exact value of sin (p-q). (p and q are acute angles) Thorough steps and details to the answer, please.
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sin p=3/5
cos p=4/5 (working with a (3-4-5) reference right triangle in quadrant I.)
tan q=5/12(working with a (5-12-13) reference right triangle in quadrant I.)
sin q=5/13
cos q=12/13
..
Identity: sin(x-y)=sinxcosy-cosxsiny
sin(p-q)=(sin p*cos q)-(cos p*sin q)=(3/5*12/13)-(4/5*5/13)=36/65-20/65=16/65
..
Calculator check:
sin p=3/5
p≈36.87˚
tan q=5/12
q=22.62˚
p-q=36.87-22.62≈14.25˚
sin(p-q)=sin (14.25˚)≈0.2462
Exact value=16/65≈0.2462