Sin Degrees Calculator

Enter an angle in degrees to get its sine, cosine, and tangent, along with the equivalent angle in radians.

Quick Facts

Degrees to radians
θ_rad = θ° × π/180
Sine is defined on radian angles internally; degrees are converted first.
Common values
sin 30°=0.5, sin 45°≈0.7071, sin 60°≈0.8660, sin 90°=1
From the 30-60-90 and 45-45-90 special right triangles.
Range
-1 ≤ sin(θ) ≤ 1
Sine never exceeds ±1 for any real angle.
Periodicity
sin(θ + 360°) = sin(θ)
The sine wave repeats every full revolution.

Your Results

Calculated
sin(θ)
-
Sine of the angle
cos(θ)
-
Cosine of the angle
tan(θ)
-
Tangent of the angle (sin/cos)
Angle in Radians
-
θ × π/180

Ready

Enter an angle in degrees, then press Calculate.

How to Find the Sine of an Angle in Degrees

In a right triangle, sin(θ) is defined as the ratio of the side opposite angle θ to the hypotenuse: sin(θ) = opposite / hypotenuse. On the unit circle, sin(θ) is simply the y-coordinate of the point where the terminal side of angle θ (measured counterclockwise from the positive x-axis) crosses the circle of radius 1. Because most math libraries — including JavaScript's Math.sin() — expect the angle in radians, this calculator first converts your degree input to radians and then evaluates the sine, cosine, and tangent.

Converting degrees to radians

A full circle is 360° or 2π radians, so 1° = π/180 radians. The conversion formula is θ_rad = θ° × π/180 (equivalently, θ_rad = θ° × π ÷ 180 ≈ θ° × 0.0174533). For example, 30° = 30 × π/180 = π/6 ≈ 0.5236 radians, and sin(π/6) = 0.5. This calculator performs that conversion automatically, so you can enter degrees directly.

Signs by quadrant

The sign of sin, cos, and tan depends on which quadrant the angle falls in after reducing it modulo 360°. In Quadrant I (0°-90°) all three are positive. In Quadrant II (90°-180°) only sine is positive. In Quadrant III (180°-270°) only tangent is positive. In Quadrant IV (270°-360°) only cosine is positive — often remembered with the mnemonic "All Students Take Calculus." Tangent is undefined at 90° and 270° (and every 180° increment from there) because cosine equals zero there, making the ratio sin/cos divide by zero.

Common mistakes

  • Mixing degrees and radians: feeding a degree value straight into a function expecting radians (or vice versa) gives a wildly wrong answer — always convert first.
  • Forgetting periodicity: sin(θ) = sin(θ + 360°n) for any integer n, so 390° and 30° give the same sine.
  • Confusing sin with arcsin: sin(θ) turns an angle into a ratio; arcsin (sin⁻¹) turns a ratio back into an angle. They are inverse operations, not the same function.

Frequently Asked Questions

How do I find the sine of an angle given in degrees?
First convert the angle to radians using radians = degrees × π/180, then apply the sine function to the radian value: sin(θ°) = sin(θ × π/180 rad). For example, sin(30°) = sin(0.5236 rad) = 0.5.
What are the sine values for common angles like 30°, 45°, 60°, and 90°?
sin(0°) = 0, sin(30°) = 0.5, sin(45°) = √2/2 ≈ 0.7071, sin(60°) = √3/2 ≈ 0.8660, and sin(90°) = 1. These come directly from the 30-60-90 and 45-45-90 special right triangles.
Why can sin(θ) be negative even though a ratio of lengths sounds positive?
On the unit circle, sine equals the y-coordinate of the point at angle θ. That coordinate is positive in Quadrants I and II (0°-180°) and negative in Quadrants III and IV (180°-360°), so sin(θ) is negative for angles like 210° or 300°.
What is the difference between sin(θ) and arcsin (sin⁻¹)?
sin(θ) takes an angle and returns a ratio between -1 and 1. Arcsin (the inverse sine, sin⁻¹) takes a ratio between -1 and 1 and returns the corresponding angle, restricted to -90° to 90° by convention.

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