SOLUTION: If cosα=4/5 and cosβ=12/13, find sin(α+β) when α and β are the measures of two first-quadrant angles. Give answer as a fraction.
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Question 515399: If cosα=4/5 and cosβ=12/13, find sin(α+β) when α and β are the measures of two first-quadrant angles. Give answer as a fraction.
Answer by drcole(72) (Show Source): You can put this solution on YOUR website!
To find , we need to use the sum formula for sine:
We have and , and we know that and are first quadrant angles, which implies that both and are positive. To find , recall the trigonometric identity:
Using what we know, we can solve for :
(substituting for )
(simplifying)
(subtracting from both sides)
(putting all terms on the right side under a common denominator)
(simplifying)
(taking the positive square root of both sides, since we know is positive)
Using the same sort of calculation, we get that . So now we substitute into the sum formula:
(substituting)
(simplifying)
(simplifying)
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