Question

Given tan x = 0.7265 and 180° `<=` x `<=` 360°, what is the value of `x`?

Answer 1

`x=216^o`

Explanation:

To begin solving this equation, we need to take the inverse of the tangent function to isolate `x`.

`tan x=0.7265 ->`
`x=tan^-1 (0.7265)`

Next, you want to calculate the value.

`x=tan^-1 (0.7265)=36^o`

Since the answer is between 180 and 360, inclusively, we need to add `180^o` to the answer to be within that range.

`x=36^o + 180^o=216^o`

The reason we do that is due to the equivalent degrees according to the unit circle. Quadrants I and III have equivalent tangent values. Quadrant III starts `180^o` greater than what is of Quadrant I, so this is why you add `180^o` to your answer.