SOLUTION: If it is known that sin a = 4/5.
pi/2 < a < pi
and that sin b = -2sqrt(5)/5
pi < b < 3pi/2 find the exact value of cos(a + b)
I am completely lost on this problem, any
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Trigonometry-basics
-> SOLUTION: If it is known that sin a = 4/5.
pi/2 < a < pi
and that sin b = -2sqrt(5)/5
pi < b < 3pi/2 find the exact value of cos(a + b)
I am completely lost on this problem, any
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Question 868372: If it is known that sin a = 4/5.
pi/2 < a < pi
and that sin b = -2sqrt(5)/5
pi < b < 3pi/2 find the exact value of cos(a + b)
I am completely lost on this problem, any and all help would be greatly appreciated Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! If it is known that sin a = 4/5.
pi/2 < a < pi ::: QII where x <0 and y > 0
Since sin = y/r, y = 4 and r = 5
Then x = -sqrt[25-16] = -3
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So cos(a) = x/r = -3/5
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and that sin b = -2sqrt(5)/5
pi < b < 3pi/2 ::: QIII where x < 0 and y < 0
Since sin = y/r, y = -2sqrt(5) and r = 5
Then x = -sqrt[25-20] = -sqrt(5)
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so cos(b) = -sqrt(5)/5
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find the exact value of cos(a + b)
cos(a+b) = cos(a)cos(b)-sin(a)sin(b)
---
= (-3/5)(-sqrt(5)/5) - (4/5)(-2sqrt(5)/5)
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Cheers,
Stan H.
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