How do you use fundamental identities to find the values of the trigonometric values given angle in quadrant 4 such that csc (theta)= -5/2?

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How do you use fundamental identities to find the values of the trigonometric values given angle in quadrant 4 such that csc (theta)= -5/2?

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Answer 1 · 2016-06-17T02:29:28

Find values of 6 trig functions

Explanation:

#csc t = - 5/2# --> #sin t = -2/5#.
Find #cos^2 t# by the identity: #cos^2 t = 1 - sin^2 t#
#cos ^2 t = 1 - 4/25 = 21/25# --> #cos t = +- sqrt21/5#
Since t in in Quadrant IV, then, cos t is positive -->
#cos t = sqrt21/5#
#tan t = sin/(cos) = (-2/5)(-5/sqrt21) = 2/sqrt21 = 2sqrt21/21#
#cot t = sqrt21/2#
#sec t = 5/sqrt21 = 5sqrt21/21#

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How do you use fundamental identities to find the values of the trigonometric values given angle in quadrant 4 such that csc (theta)= -5/2?

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