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.