the secant is the inverse of the cosine

so cos theta = 1/(sec theta) = 3/4

sin ^2 theta + cos^2 theta = 1 (basic trig identity)

sin ^2 theta + 9/16 = 1

sin ^2 theta = 7/16

sin theta = 7^0.5/4

since angle located in Quadrant IV, sin theta = -7^0.5/4

Maggie D.

asked • 06/27/20I know that theta must be in the fourth quadrant but I am lost on what identities to use for solving sin theta.

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the secant is the inverse of the cosine

so cos theta = 1/(sec theta) = 3/4

sin ^2 theta + cos^2 theta = 1 (basic trig identity)

sin ^2 theta + 9/16 = 1

sin ^2 theta = 7/16

sin theta = 7^0.5/4

since angle located in Quadrant IV, sin theta = -7^0.5/4

Robert Z. answered • 06/27/20

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Maggie D.

thank you
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06/27/20

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Maggie D.

thank you06/27/20