SOLUTION: Find values of sin(a-b)if cos a=15/17, cot b=24/7, 0 degrees<a<90 degress, and 0 degrees< b< 90 degreea

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Question 834804: Find values of sin(a-b)if cos a=15/17, cot b=24/7, 0 degrees
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find values of sin(a-b)if cos a=15/17, cot b=24/7, 0 degrees ***
sin%28a-b%29=sin%28a%29cos%28b%29-cos%28a%29sin%28b%29
cos(a)=15/17
sin%28a%29=sqrt%281-cos%5E2%28a%29%29=sqrt%281-%28225%2F289%29%29=sqrt%2864%2F289%29=8%2F17
sin(a)=8/17
..
cot(b)=24/7
hypotenuse=sqrt%2824%5E2%2B7%5E2%29=sqrt%2824%5E2%2B7%5E2%29=sqrt%28625%29=25
sin(b)=7/25
cos(b)=24/25
..
sin%28a-b%29=%288%2F17%29%2824%2F25%29-%2815%2F17%29%287%2F25%29
sin%28a-b%29=%288%2F17%29%2824%2F25%29-%2815%2F17%29%287%2F25%29=87%2F425
..
calculator check:
cos(a)=15/17
a≈28.07˚
tan(b)=7/24
b≈16.26˚
a-b≈28.07-16.26≈11.81˚
sin(a-b)=sin(11.81)≈0.2046..
exact value as calculated=87/425≈0.2047..