SOLUTION: Use the given information to determine the exact trigonometric value. If cos(theta)=4/5 and 270 degrees < theta < 360 degrees, find the exact value of sin(2theta)

Question 1032162: Use the given information to determine the exact trigonometric value.
If cos(theta)=4/5 and 270 degrees < theta < 360 degrees, find the exact value of sin(2theta)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Use the given information to determine the exact trigonometric value.
If cos(theta) = 4/5 and 270 degrees < theta < 360 degrees,
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Since cos = x/r, x = 4 and r = 5
Then y = sqrt(r^2-x^2) = sqrt(25-16) = 3
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Since t is in QIII, y is negative 3
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So sin(t) = -3/5
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find the exact value of sin(2theta) = 2*sin(t)*cos(t) = 2(-3/5)(4/5) = -24/25
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Cheers,
Stan H.
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