Calculators/Mathematics/Trigonometric Function Values

Trigonometric Function Values

sin · cos · tan · cot · degrees and radians

Trigonometric Function Values — illustration
sin
0.5
cos
0.866025
tan
0.57735
cot
1.732051

Radians: 180° = π rad. Tangent is undefined at 90°, 270°… (cos = 0), and cotangent at 0°, 180°… (sin = 0). Identity: sin²α + cos²α = 1 (Pythagorean trigonometric identity).

The calculator evaluates four trigonometric functions for a given angle: sine, cosine, tangent and cotangent. You can enter the angle in degrees or radians (180°=π180°=\pi rad).

The tangent is tan⁡α=sin⁡αcos⁡α\tan\alpha=\dfrac{\sin\alpha}{\cos\alpha} and is undefined when cos⁡α=0\cos\alpha=0 (at 90°,270°…90°, 270°\dots). The cotangent cot⁡α=cos⁡αsin⁡α\cot\alpha=\dfrac{\cos\alpha}{\sin\alpha} is undefined when sin⁡α=0\sin\alpha=0 (at 0°,180°…0°, 180°\dots).

It is worth remembering the values for special angles: sin⁡30°=12\sin30°=\tfrac12, cos⁡60°=12\cos60°=\tfrac12, sin⁡45°=cos⁡45°=22\sin45°=\cos45°=\tfrac{\sqrt2}{2}, as well as the Pythagorean identity sin⁡2α+cos⁡2α=1\sin^2\alpha+\cos^2\alpha=1.

Examples

sin 30°
→ = 0.5
tan 45°
→ = 1
cos 90°
→ = 0 (and tan 90° is undefined)

Frequently asked questions

Why is the tangent of 90° undefined?+

Because tan α = sin α / cos α, and cos 90° = 0 — division by zero. The tangent graph has a vertical asymptote there.

How do I convert degrees to radians?+

Multiply by π/180. For example 60° = 60·π/180 = π/3 rad. Conversely, radians · 180/π give degrees.

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