Sine, cosine and tangent calculator

Graph

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Formula

How it works

Sine, cosine and tangent relate an angle to the ratios of the sides of a right triangle, and extend to any angle through the unit circle. tan θ = sin θ ÷ cos θ is undefined where cos θ = 0.

Worked example

The same calculation with the default values:

• Angle 30 °

1. θ = 30 × π ÷ 180 = 0.523599 rad
2. sin θ = 0.5
3. cos θ = 0.866025
4. tan θ = 0.5 ÷ 0.866025 = 0.57735

Result: Angle in radians: 0.52359878 rad · Sine: 0.5 · Cosine: 0.8660254

Common mistakes

• Entering an angle in degrees when the field expects radians, or vice versa - this is the most common source of wildly wrong trigonometric results.
• Forgetting that tan θ is undefined at 90° (and every odd multiple of 90°) because cos θ = 0 there - a result that looks like an error at these specific angles reflects a genuine mathematical discontinuity, not a bug.
• Assuming sine and cosine values can exceed 1 or go below -1 - both are always bounded in [-1, 1]; a result outside that range signals an input or calculation error upstream.