Sine Calculator

Compute sin(x) for any angle in degrees or radians.

Inputs

Result

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General calculation reads

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How Not to Be Wrong
Jordan Ellenberg - math thinking
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The Joy of X
Steven Strogatz - accessible math
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Scientific calculator (Casio fx-991EX)
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How to use this calculator

  • Enter the angle.
  • Pick degrees or radians.
  • Read sin, plus the matching cos/tan for reference.

About this calculator

sin(x) is the y-coordinate of the point on the unit circle at angle x. Range: [−1, 1]. Period 2π. Common values: sin(0°) = 0, sin(30°) = ½, sin(45°) = √2/2 ≈ 0.707, sin(60°) = √3/2 ≈ 0.866, sin(90°) = 1.

Frequently asked

What does sin actually mean?+
For an angle in a right triangle, sin = opposite / hypotenuse. On the unit circle, sin = y-coordinate.
Why does my calculator give a tiny non-zero value for sin(180°)?+
Floating-point representation of π. sin(180°) is mathematically 0; the calculator might show 1.2e-16. The hint flags "effectively zero" when |sin| < 1e-10.
What's the period?+
2π radians (360°). sin(x + 360°) = sin(x).
How is sin different from sin⁻¹?+
sin maps angle → ratio. sin⁻¹ (arcsin) maps ratio → angle. They are inverses.
Why use radians at all?+
In calculus, the simple identity d/dx sin(x) = cos(x) holds only when x is in radians. Pure-math contexts almost always use radians.

Related calculators

Cosine Calculator
Compute cos(x) for any angle.
Tangent Calculator
tan(x) = sin(x) / cos(x). Undefined where cos(x) = 0 (at 90°, 270°, …).
Arcsine Calculator
sin⁻¹(x) — find the angle whose sine is x. Domain [-1, 1], range [−90°, 90°].
Degrees to Radians Converter
Convert any angle in degrees to radians. radians = degrees × π/180.
Radians to Degrees Converter
Convert any angle in radians to degrees. degrees = radians × 180/π.
Unit Circle Calculator
Angle θ → (cos θ, sin θ) coordinates on the unit circle. Reference angle + quadrant.

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