math (trig)

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if cos 2 theta = -(1/3) and theta is in Quadrant 2, find sin theta, cos theta, tan theta, and draw triangle theta

• math (trig) -

-1/3 = cos 2theta = 1 - 2 sin^2 theta
2 sin^2 theta = 4/3
sin theta = sqrt(2/3)
cos theta = sqrt(1 - 2/3) = -sqrt(1/3)
(minus since theta must be in quadrant 2)

tan theta = -sqrt2

theta = 125.26 degrees

You draw the figure

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