# Graphs of Sine, Cosine and Tangent

*A sine wave made by a circle:*

*A sine wave produced naturally by a bouncing spring:*

## Plot of Sine

The Sine Function has this beautiful up-down curve (which repeats every 2π radians, or 360°).

It starts at **0**, heads up to **1** by π/2 radians (90°) and then heads down to **−1**.

## Plot of Cosine

Cosine is just like Sine, but it starts at 1 and heads down until π radians (180°) and then heads up again.

## Plot of Sine and Cosine

In fact Sine and Cosine are like **good friends**: they follow each other, exactly π/2 radians (90°) apart.

## Plot of the Tangent Function

The Tangent function has a completely different shape ... it goes between negative and positive Infinity, crossing through 0, and at every π radians (180°), as shown on this plot.

At π/2 radians (90°), and at −π/2 (−90°), 3π/2 (270°), etc, the function is officially **undefined**, because it could be **positive Infinity** or** negative Infinity**.

## Inverse Sine, Cosine and Tangent

The Inverse Sine, Cosine and Tangent graphs are:

Inverse Sine

Inverse Cosine

Inverse Tangent

### Mirror Images

Here is **Cosine** and **Inverse Cosine** plotted on the same graph:

Cosine and Inverse Cosine

They are mirror images (about the diagonal)!

The same is true for **Sine** and **Inverse Sine** and for **Tangent** and **Inverse Tangent**. Can you see this in the graphs above?