Question

How do you solve `tanx=4` and find all solutions in the interval `[0,2pi)`?

Answer 1

`x=1.3528,4.4674`

Explanation:

To solve use, use the inverse tangent function:

`tan(x)=4`

`=>x=arctan(4)=1.3258`

However, this is only the angle `x` where `tan(x)=4` that is in the first quadrant. There is another angle `x` where `tan(x)=4` that is in the third quadrant, where tangent is also positive.

The angle in the third quadrant whose reference angle is `1.3258` is going to be `pi+1.3258=4.4674`.