Trigonometric Identity Explorer
Trigonometric Identity Explorer
Drag the point around the arc or use the slider to change θ. Every ratio, every identity, and every proof step updates live — so the class sees the identities hold true at every single angle, not just the textbook ones.
Drag the amber point on the arc for a hands-on feel, or click a preset to jump straight to the standard-angle table values.
The six ratios at this angle
| Ratio | Definition | Value |
|---|---|---|
| sinθ | opposite / hypotenuse | |
| cosθ | adjacent / hypotenuse | |
| tanθ | opposite / adjacent | |
| cosecθ | 1 / sinθ | |
| secθ | 1 / cosθ | |
| cotθ | 1 / tanθ |
Prove it live
Trigonometry Table Challenge
Trigonometry Memory Lab
sin: √0, √1, √2, √3, √4 — all ÷ 2
cos: read the same sequence backwards
| θ | 0° | 30° | 45° | 60° | 90° |
|---|---|---|---|---|---|
| sin | 0 | 1/2 | √2/2 | √3/2 | 1 |
| cos | 1 | √3/2 | √2/2 | 1/2 | 0 |
| tan | 0 | 1/√3 | 1 | √3 | Not defined |
Trigonometry Question Simulation and Challenge
It’s built around five NCERT-style scenarios — tower/tree, ladder against a wall, kite string, building & car (depression), lighthouse & ship (depression) — with two modes:
Heights and Distances
Explore how a right triangle links an angle of elevation or depression to a height and a distance — then try problems in the style of NCERT’s Applications of Trigonometry chapter.