Question

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

Answer 1

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.