SOLUTION: If sin P=12/13 and cos Q=3/5 and both are acute angles,determine without the use of calculator the value of cos (P+Q)
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Question 757903: If sin P=12/13 and cos Q=3/5 and both are acute angles,determine without the use of calculator the value of cos (P+Q) Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! If sin P=12/13 and cos Q=3/5 and both are acute angles,determine without the use of calculator the value of cos (P+Q)
Identity: cos(P+Q)=cos P cos Q-sin P sin Q
..
given sin P=12/13
cos P=√(1-sin^2 P)
=√(1-(12/13)^2)
=√(1-144/169)
=√(25/169)
=5/13
..
given cos Q=3/5
sin Q=√(1-cos^2 Q)
=√(1-(3/5)^2)
=√(1-9/25)
=√(16/25)
=4/5
..
cos(P+Q)=cos P cos Q-sin P sin Q
=5/13*3/5-12/13*4/5
=15/65-48/65
=-33/65
..
Calculator check:
sin P=12/13
P≈67.38º
cos Q=3/5
Q≈53.13
P+Q≈67.38+53.13≈120.51º
cos(P+Q)≈cos(120.51)≈-0.5076..
exact value=-33/65≈-0.5076..
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