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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