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