How do you find the exact value of cos(u−v) given that sinu=5/13 and cosv=-3/5

saillantpq

saillantpq

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2022-08-31

How do you find the exact value of cos ( u v ) given that sin u = 5 13 and cos v = 3 5 ?

Answer & Explanation

elgrupomentasb

elgrupomentasb

Beginner2022-09-01Added 9 answers

Find cos u using Pythagorean Theorem to find the adjacent side. Assume angle u is in the first quadrant:
1. 13 2 = 5 2 + a 2
2. a 2 = 169 25 = 144
3. a=12
So cos u = 12 13
Find sin v using Pythagorean Theorem to find the adjacent side. Assume angle v is in the second quadrant:
1. ( 3 ) 2 + b 2 = 5 2
2. b 2 = 25 9 = 16
3. b=4
So sin v = 4 5
Use the difference formula cos ( u v ) = cos u cos v + sin u sin v :
cos ( u v ) = 12 13 3 5 + 5 13 4 5 = 36 65 + 20 65 = 16 65

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