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
• 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 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.