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θ
Trigonometry
sin, cos, tan with a visual unit circle and SOHCAHTOA special values.
Unit
0°30°360°
cossintan
Angle: 30°(0.5236 rad)
sin
1/2
0.5
cos
√3/2
0.866
tan
√3/3
0.5774
csc
2
sec
1.1547
cot
1.7321
Examples
How to use it
The unit circle — the foundation of trigonometry. The angle is measured from the positive x-axis, anticlockwise. The point on the circle is (cos θ, sin θ), and tan θ is the ratio sin/cos (also the distance along the line x=1).
- Example 1 — sin 30°: in a 30-60-90 triangle the side opposite the 30° angle is half the hypotenuse, so sin 30° = 1/2.
- Example 2 — cos 45°: in a 45-45-90 triangle the two shorter sides are equal, so cos 45° = sin 45° = √2/2.
- Example 3 — tan 60°: tan 60° = sin 60° / cos 60° = (√3/2)/(1/2) = √3 ≈ 1.7321.
💼 Triangles, structures, waves and music (frequencies) — trigonometry sits behind every periodic phenomenon.
Related tools
- Pythagoras' theorem — the basis for spotting a 30-60-90 or 45-45-90 triangle.
- Function grapher — plot sin and cos waves and see the periodicity.
- Quadratic equation solver — square roots, directly linked to values like √2/2 and √3/2.
✍️ Written by the MathsUK teamChecked against the National Curriculum and GCSE specifications