# How do you solve #Tan 3x = -1#?

##### 1 Answer

The answer is 135°; any other angle can be found by remembering the periodicity of the tan-function, that is to say, 180°.

#### Explanation:

By applying the mathematical definition of tangent:

By using our demanded value:

By applying the trigonometric property:

By using a calculator, the easy way, or interpolation, the hard way, we get:

Remembering

we get the "basal" value: 135°. and apply:

where n is integer, you can get any other solution.

PS: there is a nice thing to do, a trick I used to apply to my private students, I will try to make a diagram, you can find the basic angles such as the one just presented herein, easily to remember.