Answer: 220/221
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Work Shown:
The given values are
- sin(u) = -12/13
- cos(v) = -8/17
Through the Pythagorean trig identity, we can find
- cos(u) = -5/13
- sin(v) = -15/17
I'm skipping these steps, but let me know if you need me to go over them.
Since u and v are in quadrant 3, this means both sine and cosine are negative here
Using those four items, we can then say the following:
cos(v-u) = cos(v)cos(u) + sin(v)sin(u)
cos(v-u) = (-8/17)*(-5/13) + (-15/17)*(-12/13)
cos(v-u) = 40/221 + 180/221
cos(v-u) = (40 + 180)/221
cos(v-u) = 220/221
This is reduced as much as possible because the GCF of n and n+1 is always 1.
