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) (Show Source): You can put this solution on YOUR website!
We know by our double angle formulas that
We are given that So construct a triangle with adjacent side 3 and hypotenuse 5. Then following the Pythagorean Theorem, the opposite side of is 4.
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Thus,
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So,
Answer by stanbon(75887) (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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