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Angle α lies in quadrant II , and tanα=−12/5 . Angle β lies in quadrant IV , and cosβ=3/5 . What is the exact value of cos(α−β) ?

 Apr 1, 2020
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cos(a - b)  = cos(a)·cos(b) + sin(a)·sin(b)

 

Since tan(a)  =  -12/5  and is in quadrant II, sin(a) = 12/13  and  cos(a) = -5/13

  (It's a 5-12-13 right triangle, with x-value negative and y-value positive.)

 

Since cos(b)  =  3/5  and is in quadrant IV, sin(b)  =  -4/5.

  (It's a 3-4-5 right triangle, with x-value positive and y-value negative.)

 

Place these values into the formula to get your answer.

 Apr 1, 2020

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