Sin Degrees Calculator — Sine of an Angle in Degrees
Type any angle in degrees and instantly get its sine — plus cosine, tangent and the radian equivalent — with six decimal precision.
°
Sine of the degree angle — always between −1 and 1
- 1
Convert to radians
45 × π ÷ 180 = 0.785398 - 2
Compute sin(θ°)
sin(0.785398) = 0.707107
How does this calculator work?
sin(θ°) converts θ to radians via θ × π/180, then evaluates sine. The result is always in [−1, 1]. Key values: sin(0°) = 0, sin(30°) = 0.5, sin(45°) ≈ 0.707, sin(60°) ≈ 0.866, sin(90°) = 1. The function repeats every 360°.
Formula
How this is calculated
Trigonometric functions are defined on the unit circle in radians, so a degree input θ is first multiplied by π/180 to obtain the radian equivalent before the standard sine function is evaluated. This conversion is exact for all representable floating-point values; sin(30°) = sin(π/6) = 0.5, sin(45°) = √2/2 ≈ 0.7071, sin(60°) = √3/2 ≈ 0.8660, sin(90°) = 1.
Sine is the y-coordinate of the point on the unit circle at the given angle, measured counter-clockwise from the positive x-axis. In a right triangle it equals the length of the side opposite the angle divided by the hypotenuse. It is periodic with period 360° and always lies in [−1, 1].
The Pythagorean identity sin²(θ) + cos²(θ) = 1 is displayed as a check — it should always equal 1 (any deviation from 1 would be floating-point rounding, on the order of 10⁻¹⁶).
Frequently asked questions
sin(90°) = 1. At 90°, the point on the unit circle is at the top (0, 1), giving the maximum y-coordinate. In a right triangle, the 90° angle is the right angle, and the side opposite it is the hypotenuse, so opposite/hypotenuse = hypotenuse/hypotenuse = 1.
All three equal zero (or very close to zero due to floating-point). At 0° and 360° the unit-circle point is (1, 0) with y = 0; at 180° the point is (−1, 0), also with y = 0. Sine crosses zero at every multiple of 180°.
Yes. Sine is periodic, so sin(−30°) = −sin(30°) = −0.5, and sin(390°) = sin(30°) = 0.5. Negative angles measure clockwise rotation on the unit circle; angles beyond 360° simply wrap around.
TG we-Calculate Editorial Team. (2026). Sin Degrees Calculator — Sine of an Angle in Degrees [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/sin-degrees-calculator
TG we-Calculate Editorial Team. "Sin Degrees Calculator — Sine of an Angle in Degrees." TG we-Calculate. 2026. https://we-calculate.com/calculator/sin-degrees-calculator.
TG we-Calculate Editorial Team, "Sin Degrees Calculator — Sine of an Angle in Degrees," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/sin-degrees-calculator
@misc{wecalculate_sin_degrees_calculator, title = {Sin Degrees Calculator — Sine of an Angle in Degrees}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/sin-degrees-calculator}}, year = {2026}, note = {TG we-Calculate} }
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