sin(θ) Calculator — Sine of Theta
Enter angle θ in degrees or radians to find sin(θ) — displayed with the unit-circle (x, y) coordinates, cosine, tangent and cosecant.
°
Angle unit
y-coordinate of the unit-circle point at angle θ
- 1
Convert to radians
30 × π ÷ 180 = 0.523599 - 2
Compute sin(θ)
sin(0.523599) = 0.500000
How does this calculator work?
sin(θ) = y on the unit circle = opposite/hypotenuse in a right triangle. Always in [−1, 1], period 360°. Enter θ in degrees or radians; cos(θ), tan(θ) and csc(θ) are shown alongside. Key values: sin(30°) = 0.5, sin(45°) ≈ 0.707, sin(90°) = 1.
Formula
How this is calculated
The sine function sin(θ) maps an angle θ to the y-coordinate of the point where the angle's terminal ray meets the unit circle (radius 1 centred at the origin). In a right triangle the same value equals the length of the side opposite the angle divided by the hypotenuse. Degree input is converted to radians via rad = θ × π/180 before evaluation, because JavaScript's Math.sin operates in radians.
The unit-circle (x, y) coordinates are (cos θ, sin θ). Together they satisfy the Pythagorean identity x² + y² = 1 for every angle, verifying that the calculator's values are internally consistent. Cosecant — the reciprocal 1/sin θ — is displayed alongside; it is undefined wherever sin θ = 0 (multiples of 180°).
Sine is periodic with period 2π (360°) and bounded in [−1, 1]. The animated waveform shows one full sine cycle with the phase offset set to your angle θ so you can see exactly where on the wave your value sits.
Frequently asked questions
sin(θ) is the y-coordinate of the point on the unit circle at angle θ. Equivalently, in a right triangle it is the ratio of the side opposite the angle to the hypotenuse. Its value ranges from −1 (at θ = −90° / 270°) to +1 (at θ = 90°).
sin(0°) = 0, sin(30°) = 1/2, sin(45°) = √2/2 ≈ 0.7071, sin(60°) = √3/2 ≈ 0.8660, sin(90°) = 1. These "exact values" come from 30-60-90 and 45-45-90 triangle geometry.
csc(θ) = 1/sin(θ). At 0° and 180°, sin(θ) = 0, so 1/0 is undefined. The calculator shows "undefined" at those angles rather than an erroneous large number.
TG we-Calculate Editorial Team. (2026). sin(θ) Calculator — Sine of Theta [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/sin-theta-calculator
TG we-Calculate Editorial Team. "sin(θ) Calculator — Sine of Theta." TG we-Calculate. 2026. https://we-calculate.com/calculator/sin-theta-calculator.
TG we-Calculate Editorial Team, "sin(θ) Calculator — Sine of Theta," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/sin-theta-calculator
@misc{wecalculate_sin_theta_calculator, title = {sin(θ) Calculator — Sine of Theta}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/sin-theta-calculator}}, year = {2026}, note = {TG we-Calculate} }
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