SOLUTION: If cos θ = 3/5 and θ terminates in the first quadrant, find the exact value of sin 2θ.

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Question 445214: If cos θ = 3/5 and θ terminates in the first quadrant, find the exact value of sin 2θ.
Found 2 solutions by swincher4391, stanbon:
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
We know by our double angle formulas that sin%282theta%29+=+2sin%28theta%29cos%28theta%29
We are given that cos%28theta%29+=+3%2F5 So construct a triangle with adjacent side 3 and hypotenuse 5. Then following the Pythagorean Theorem, the opposite side of theta is 4.
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Thus, sin%28theta%29+=+4%2F5
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So, sin%282theta%29+=+2%2A%284%2F5%29%2A%283%2F5%29+=+highlight%2824%2F25%29

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
If cos θ = 3/5 and θ terminates in the first quadrant,
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Since cos = x/r, x = 3 and r = 5
Then y = sqrt(5^2-3^2) = sqrt(16) = 4
So sin(theta) = 4/5
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find the exact value of sin 2θ
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sin(2*theta) = 2sin(theta)*cos(theta)
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= 2*(4/5)(3/5) = 24/25
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Cheers,
Stan H.
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