SOLUTION: find the exact value of cos(u-v) given that sin u = -(12/13) and cos v = -(3/5) and both u and v are in QIII

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Question 1085621: find the exact value of cos(u-v) given that sin u = -(12/13) and cos v = -(3/5) and both u and v are in QIII
Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.
1.  Since sin(u) = -12%2F13, cos(u) = sqrt%281-sin%5E2%28u%29%29 = sqrt%281-%28-12%2F13%29%5E2%29 = sqrt%281-144%2F169%29 = sqrt%28%28169-144%29%2F169%29 = +/- 5%2F13.

   Since "u" is in Q3, cos(u) is negative, and we have cos(u) = -5%2F13.


2.  Similarly, sin(v) = sqrt%281-cos%5E2%28v%29%29 = -4%2F5.


3.  Now, cos(u-v) = cos(u)*cos(v) + sin(u)*sin(v) = %28-5%2F13%29%2A%28-3%2F5%29+%2B+%28-12%2F13%29%2A%28-4%2F5%29 = 15%2F65+%2B+48%2F65 = 63%2F65.


Answer. 63%2F65.

Solved.


To see more solved similar problems on calculating trig functions look into the lessons
    - Calculating trigonometric functions of angles
    - Advanced problems on calculating trigonometric functions of angles
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Trigonometry: Solved problems".