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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