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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,

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.