How do you find the exact value of cot(u+v) given that sinu=513 and cosv=−35?
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Explanation:
Find cosu using Pythagorean Theorem to find the adjacent side. Assume angle u is in the first quadrant:
132=52+a2
a2=169−25=144
a=12
So cosu=1213
Find sinv using Pythagorean Theorem to find the adjacent side. Assume angle v is in the second quadrant:
(−3)2+b2=52
b2=25−9=16
b=4
So sinv=45
Use the difference formula cos(u−v)=cosucosv+sinusinv:
cos(u−v)=1213⋅−35+513⋅45=−3665+2065=−1665
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