# calculus

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What is the exact value of sin(2 theta) if cos (theta)=3/5 and (theta) is in quadrent 4?

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• calculus -

cos(theta) = 3/5

cos-1(3/5) = theta = 53.13 degrees
This is the value that your calculator gives, and it is in quadrant; To find the value theta corresponding to quadrant 4, notice the symmetry in a graph of cos x, which is that cos(x), cos(x) = cos(360 - x); 306.87 = theta in quadrant 4
quadrant 1 (0 - 90 degrees)
quadrant 2 (90 - 180 degrees)
quadrant 3 (180 - 270 degrees)
quadrant 4 (270 - 360 degrees)

Use your calculator to calculator sin(2*306.87)

• calculus -

-24/25

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