Sin Calculator
Calculate sine values in degrees and radians with step-by-step calculations and unit circle references. Perfect for trigonometry, mathematics, and engineering applications.
Sine Calculator
Common Sine Values
Click on these links to see instant calculations with common angles:
Sine Function
The sine function is a fundamental trigonometric function that relates an angle to the ratio of the opposite side to the hypotenuse in a right triangle. On the unit circle, sine represents the y-coordinate.
Sine Properties
Range: [-1, 1]
Period: 360° (2π radians)
sin(θ) = opposite / hypotenuse
sin(-θ) = -sin(θ) (odd function)
sin(θ + 360°) = sin(θ) (periodic)
Common Sine Values
| Angle (Degrees) | Angle (Radians) | Sine Value | Exact Value |
|---|---|---|---|
| 0° | 0 | 0 | 0 |
| 30° | π/6 | 0.5 | 1/2 |
| 45° | π/4 | 0.707 | √2/2 |
| 60° | π/3 | 0.866 | √3/2 |
| 90° | π/2 | 1 | 1 |
| 120° | 2π/3 | 0.866 | √3/2 |
| 135° | 3π/4 | 0.707 | √2/2 |
| 150° | 5π/6 | 0.5 | 1/2 |
| 180° | π | 0 | 0 |
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- Mathematics: Solve trigonometric equations and geometric problems
Frequently Asked Questions
What is the sine function?
The sine function (sin) is a trigonometric function that relates an angle in a right triangle to the ratio of the opposite side to the hypotenuse. In the unit circle, sin(θ) represents the y-coordinate of the point.
What is the range of the sine function?
The range of the sine function is [-1, 1]. This means sine values are always between -1 and 1, inclusive. The function oscillates between these values as the angle changes.
What are the common sine values?
Common sine values include: sin(0°) = 0, sin(30°) = 1/2, sin(45°) = √2/2 ≈ 0.707, sin(60°) = √3/2 ≈ 0.866, sin(90°) = 1. These correspond to special angles on the unit circle.