If sin θ = 1/2 and angle θ is acute, how do you find the other five ratios?

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Answer 1 · 2018-04-02T11:54:37

#color(green)(cos theta = sqrt3 / 2, sec theta = 2 / sqrt3, csc theta = 2, tan theta = 1 / sqrt3, cot theta = sqrt3#

#"Given " sin theta = 1/2, " and the angle is acute or less than " 90^2 " which lies in the first quadrant.

This makes all the trigonometric functions positive.

#cos^2 theta = 1 - sin^2 theta = 1 - 1/4 = 3/4#

Hence, #cos theta = sqrt3 / 2#

#tan theta = sin theta / cos theta = (1/2) / ( sqrt3 / 2) = 1/ sqrt3#

#cot theta = 1 / tan theta = 1 (1/sqrt3) = sqrt 3#

#csc theta = 1 / sin theta = 1 (1/2) = 2#

#sec theta = 1 / cos theta = 1 / (sqrt3 / 2) = 2 / sqrt3#