The sine of an angle is the ratio of the side opposite the angle to the hypotenuse of a right triangle; on the unit circle it is the y-coordinate of the point at angle α. Sine waves describe sound, light, alternating current, tides and every kind of oscillation.
How to use the Sine Calculator
- Angle unit
- Angle α
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Enter the angle and pick its unit. The angle is converted to radians and sin is evaluated; for multiples of 15° the exact value with square roots is shown as well (for example √3/2). Where the function is undefined, the calculator says so instead of printing a huge number.
Formula
sin α = opposite / hypotenuse = y-coordinate on the unit circle
Range: [−1, 1] · Domain: all real numbers · Period: 2π (360°)
Worked example
Inputs — Angle unit: Degrees (°); Angle α: 30.
Results — sin(α) = 1/2 ≈ 0.5; cos(α) = √3/2 ≈ 0.8660254038; tan(α) = √3/3 ≈ 0.5773502692; csc(α) = 2; sec(α) = 1.154700538; cot(α) = 1.732050808.
Key terms
- Sine
- sin α = opposite / hypotenuse = y-coordinate on the unit circle.
- Exact value
- A value written with integers and square roots instead of decimals.
Frequently asked questions
What is sin 30°?
Exactly 1/2.
What is sin 90°?
1, the largest value sine takes.
Is sine positive in the second quadrant?
Yes – sine is positive in quadrants I and II and negative in III and IV.
How do I get the angle back from a sine value?
Use arcsin; remember that a second angle 180° − α has the same sine.