SOLUTION: sin u = −5/13 and cos v = −15/17 (Both u and v are in Quadrant III.) what is cos(u+v)

Algebra ->  Trigonometry-basics -> SOLUTION: sin u = −5/13 and cos v = −15/17 (Both u and v are in Quadrant III.) what is cos(u+v)      Log On


   

Question 1147426: sin u = −5/13
and
cos v = −15/17
(Both u and v are in Quadrant III.)
what is cos(u+v)
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


5-12-13 and 8-15-17 are Pythagorean Triples. So

sin u = -5/13 in quadrant III --> cos u = -12/13
cos v = -15/17 in quadrant III --> sin v = -8/17

Then

cos%28u%2Bv%29+=+cos+u+%2A+cos+v+-+sin+u+%2A+sin+v

Use a calculator....

Answer by ikleyn(52824) About Me  (Show Source):
You can put this solution on YOUR website!
.

This problem IS NOT about getting "the value".


It is about getting the answer in the form of a fraction.


So, you need substitute the fractions into the formula and calculate and present

the answer as a fraction.


cos(u+v) = cos(u)*cos(v) - sin(u)*sin(v) = %28-12%2F13%29%2A%28-15%2F17%29+-+%28-5%2F13%29%2A%28-8%2F17%29 = %2812%2A15%29%2F%2813%2A17%29+-+%285%2A8%29%2F%2813%2A17%29 = %2812%2A15+-+5%2A8%29%2F%2813%2A17%29 = 140%2F221.    ANSWER


It is THE expected form of the solution and the answer to this problem.

Solved.