# Tangent

Concept

In this course, we will be looking at general solutions of tangent , where k is a real number

There is always a value between and such that tangent (k has to be a real number). This value is known as the principal value of . is known as the principal solution of . The intersection of the line and the tangent graph shows that are also solutions of tangent .

The general expression of these solutions is given by = , Z

This is called the general solution of tangent

If the solution is required in degrees, then the general solution is , Z

Scholar's Tip: If , the general solution would be , Z

Examples

Find the general solution to the following tangent equations.

a) tangent b) tangent

a) This is similar to solving for the general solution of other trigonometry functions. We have to convert into its tangent form.

tangent tangent

, Z

b) Let's try it out when degrees are involved.

tangent

, Z

You may want to look at sine, cosine solutions as well . There is also the law of sines and law of cosines .