# Why are the tangents for 90 and 270 degrees undefined?

##### 2 Answers

This is a good question indeed!

#### Explanation:

I'll try to give you a visual explanation.

Consider the trigonometric meaning of tangent of an angle

The tangent of

Hope it helps!

You can also say that

*You can take a look at the overlap of #sinx# and #cosx# below to see what happens to each as we approach #90^o# and #270^o# from the right or left:*

graph{(y - sinx)(y - cosx) = 0 [-0.034, 6.2831, -1.2, 1.2]}

We can establish that:

because

because *both*

We can also see that:

because

because *both*

**Since the limits from the left and right side are not the same, #\mathbf(tanx)# of those angles is undefined.**