Asked by Anonymous
Use the given information to evaluate cos (a+b). Sin a = -7/25, cot b = -8/15. Neither a nor b are in quadrant IV. exact answers only. No decimals.
Answers
Answered by
Reiny
since the sine is negative in III or IV and the cotangent is negative in II or IV, and we are told that neither is in IV
a must be in III and b must be in II
sin a = -7/25, a in III
cos a = -24/25
cot b = -8/15 , b in II
tan b = -15/8
sinb = 15/17
cosb = -8/17
cos(a+b)
= cosa cosb - sina sinb
= (-24/25)(-8/17) - (-7/25)(15/17)
= 297/425
a must be in III and b must be in II
sin a = -7/25, a in III
cos a = -24/25
cot b = -8/15 , b in II
tan b = -15/8
sinb = 15/17
cosb = -8/17
cos(a+b)
= cosa cosb - sina sinb
= (-24/25)(-8/17) - (-7/25)(15/17)
= 297/425
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