How do you find the value of #sectheta# if #cottheta=3/4# for #180^circ<=theta<=270^circ#?

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Answer 1 · 2017-01-12T23:30:51

Use the identities #tan(theta) = 1/cot(theta) and sec^2(theta) = 1 + tan^2(theta)#

#tan(theta) = 1/cot(theta)#

#tan(theta) = 4/3#

Substitute #(4/3)^2# for #tan^2(theta)# into the identity #sec^2(theta) = 1 + tan^2(theta)#:

#sec^2(theta) = 1 + (4/3)^2#

#sec^2(theta) = 25/9#

#sec(theta) = +-5/3#

We know that the secant is negative in the specified quadrant:

#sec(theta) = -5/3#