How do you find the exact value given that tan(x)=1/2 from pi<x<3pi/2?

1 Answer
Jim H
Apr 15, 2015

Because I do not know a special angle (number) whose tangent is 1/2, I'll have to write the answer using the inverse tangent function, arc tan or tan^-1.

tan^-1(1/2) = t where tant = 1/2 and -pi/2 < t < pi/2

Since tan t >0, we can further say: 0 < t < pi/2

The value ox x in pi < x < (3 pi)/2 (in quadrant 3), with reference angle t, is:

pi + t, so we write the answer:

pi + tan^-1 (1/2) or pi + arctan(1/2)

depending on your notation for the inverse trigonometric functions.

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