# Trigonometric Ratios - Interactive Graph

The previous page claimed these 2 trigonometric identities are correct, for any angle.

`tan theta = (sin theta) / (cos theta)`, and

`sin^2 theta + cos^2 theta = 1`

In the interactive graph below you can explore why these trigonometric identities are true.

For background information on what's going on, and more explanation, see the previous page,

Continues below ⇩

## Interactive Graph - Circle and trig identities

You can explore the identities `tan theta = (sin theta) / (cos theta)` and `sin^2 theta + cos^2 theta = 1` in the following JSXGraph (it's not a fixed image).

### Things to do

1. Drag point P around the circle.

2. Observe the values given for `sin theta`, `cos theta` (and their squares), and `tan theta` for different angles.

3. Observe the `x`- and `y`-values for the point P in the (light gray) tooltip that appears as you drag.

Hopefully you can see that:

`tan theta = (sin theta) / (cos theta)`

and

`sin^2 theta + cos^2 theta = 1`

for any angle `theta`.

**NOTE:** The circle in the above graph has radius 5. The trigonometric ratios work for a circle of any radius.

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