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,

Trigonometric Identities

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.