Cosine Calculator
Compute cos(θ) in degrees, radians, or gradians. Shows exact values for common angles, unit-circle visualization, and related angle info.
Angle
Updates as you typeUnit
Measurement unit ?
Angle
Angle (θ) ?
—
°
Quick angles ?
Keyboard: focus the input then ←/→ to nudge 1°, Shift+←/→ for 15°. D/R/G switch units.
Cosine wave
y = cos(θ)The cosine wave repeats every 360° (period 2π). The dot marks your current angle; negative or large values wrap naturally into this window.
Show the working
Common angles reference
Your current angle is highlighted| Deg | Rad | sin | cos | tan | cot |
|---|
Formula
cos(θ)
=
adjacent
hypotenuse
Unit circle: cos(θ) is the x-coordinate of the point reached by rotating an angle θ counter-clockwise from the positive x-axis on a circle of radius 1.
Range & period: cos(θ) ∈ [−1, 1] for every real θ, and cos(θ + 360°) = cos(θ). Cosine is also even: cos(−θ) = cos(θ).
- θ
- The angle. Degrees, radians, or gradians — the calculator normalises both ways so you can type either.
- Adjacent
- The right-triangle side touching θ that is not the hypotenuse.
- Hypotenuse
- The longest side of the right triangle — opposite the right angle.
- Reference angle
- The acute angle between the terminal side and the nearest x-axis. Cosine of θ and its reference angle share the same magnitude; only the sign changes with the quadrant.
Worked example — your numbers
- Angle θ = —
- Convert to radians = —
- Quadrant = — → sign of cos is —
- Reference angle = —
- cos(ref) = —
- cos(θ) = —
When θ is one of the canonical angles (0°, 30°, 45°, 60°, 90°, …), the calculator shows the exact value (e.g. √2/2). Otherwise it falls back to a high-precision decimal.