SOLUTION: Find the exact value of the trigonometric function given that sin(u) = 12/13 and cos(v) = -4/5. (Both u and v are in Quadrant II.) cos(v − u)

Algebra ->  Trigonometry-basics -> SOLUTION: Find the exact value of the trigonometric function given that sin(u) = 12/13 and cos(v) = -4/5. (Both u and v are in Quadrant II.) cos(v − u)       Log On


   

Question 297915: Find the exact value of the trigonometric function given that sin(u) = 12/13 and cos(v) = -4/5. (Both u and v are in Quadrant II.)
cos(v − u)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
cos%28v-u%29+=+cos%28v%29%2Acos%28u%29+%2B+sin%28x%29%2Asin%28y%29+
.
.
.
sin%28u%29+=+12%2F13
sin%5E2%28u%29%2Bcos%5E2%28u%29=1
%2812%2F13%29%5E2%2Bcos%5E2%28u%29=1
144%2F169%2Bcos%5E2%28u%29=169%2F169
cos%5E2%28u%29=%28169-144%29%2F169
cos%5E2%28u%29=25%2F169
cos%28u%29=0+%2B-+5%2F13
Quadrant II
cos%28u%29+=+-5%2F13
.
.
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cos%28v%29=-4%2F5
sin%5E2%28v%29+%2Bcos%5E2%28v%29=1
sin%5E2%28v%29%2B%28-4%2F5%29%5E2=1
sin%5E2%28v%29%2B%2816%2F25%29=25%2F25
sin%5E2%28v%29=%2825-16%29%2F25
sin%5E2%28v%29=9%2F25
sin%28v%29=0+%2B-+3%2F5
Quadrant II
sin%28v%29=3%2F5
Now substitute directly,
cos%28v-u%29+=+cos%28v%29%2Acos%28u%29+%2B+sin%28v%29%2Asin%28u%29+
cos%28v-u%29+=+-%284%2F5%29%2A%28-%285%2F13%29%29+%2B+%283%2F5%29%2A%2812%2F13%29+
cos%28v-u%29+=+20%2F65%2B+36%2F65+
cos%28v-u%29+=+56%2F65+