Graphs of Sine, Cosine and Tangent

A sine wave made by a circle:

A sine wave produced naturally by a bouncing spring:

Graph 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.

Graph of Cosine

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

Graph of Sine and Cosine

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

Graph of the Tangent Function

The tangent function has a completely different shape:

• it goes between negative and positive infinity
• and crosses through y=0 at x=0 and every π radians (180°)

Halfway between those zero points (such as at π/2 radians (90°) the function is officially undefined.

Why 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's 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.