SOLUTION: For sin α = -3/5 with terminal side in QIII and tan β = -5/12 with terminal side in QIV, find cos(α-β) a.63/65 b.33/65 c.-33/65 d.-63/65

Algebra ->  Finance -> SOLUTION: For sin α = -3/5 with terminal side in QIII and tan β = -5/12 with terminal side in QIV, find cos(α-β) a.63/65 b.33/65 c.-33/65 d.-63/65      Log On


   

Question 1079893: For sin α = -3/5 with terminal side in QIII and tan β = -5/12 with terminal side in QIV, find cos(α-β)
a.63/65
b.33/65
c.-33/65
d.-63/65
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+cos%28+a+-+b+%29+=+cos%28a%29%2Acos%28b%29+%2B+sin%28a%29%2Asin%28b%29+
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In the 3rd quadrant, the cosine is negative
and the sides are 3-4-5, so if
+sin%28a%29+=+-3%2F5+
+cos%28a%29+=+-4%2F5+
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In the 4th quadrant, sine is negative
and cosine is positive.
This sides are 5, 12, 13 , so
+sin%28b%29+=+-5%2F13+
+cos%28b%29+=+12%2F13+
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+cos%28+a+-+b+%29+=+cos%28a%29%2Acos%28b%29+%2B+sin%28a%29%2Asin%28b%29+
+cos%28+a+-+b+%29+=+%28+-4%2F5+%29%2A%28+12%2F13+%29+%2B+%28+-3%2F5%29%2A%28+-5%2F13+%29+
+cos%28+a+-+b+%29+=+%28+-48%2F65+%29+%2B+15%2F65+
+cos%28+a+-+b+%29+=+-33%2F65+
The answer is (C)