Sine Calculator
Calculate sin(x) for any angle
Common Sine Values
0°
0
30°
0.5 (1/2)
45°
√2/2 ≈ 0.707
60°
√3/2 ≈ 0.866
90°
1
180°
0
270°
-1
360°
0
About Sine Function
The sine function is one of the fundamental trigonometric functions. In a right triangle, sine of an angle is the ratio of the opposite side to the hypotenuse.
Definition
For a right triangle: sin(θ) = opposite / hypotenuse
On the unit circle: sin(θ) = y-coordinate of the point on the circle
Properties
- Range: −1 ≤ sin(θ) ≤ 1
- Period: 360° (2π radians)
- sin(0°) = 0, sin(90°) = 1
- sin(θ + 360°) = sin(θ)
- sin(−θ) = −sin(θ) (odd function)
Applications
- Physics: Wave motion, oscillations
- Engineering: Signal processing, AC circuits
- Navigation: Distance and position calculations
- Architecture: Structural design
- Music: Sound waves, frequencies
How to Use This Calculator
Enter the Angle
Input the angle value you want to calculate the sine for. You can use degrees or radians.
Select Unit
Choose whether your angle is in degrees (°) or radians (rad).
Calculate
Click the "Calculate Sine" button to get the result instantly.
Review Results
View the sine value along with the angle in both degrees and radians, plus related trigonometric values.
Formula
sin(θ) = opposite / hypotenuse
In a right triangle
Unit Circle Definition:
sin(θ) = y-coordinate on unit circle
Key Relationships:
- sin²(θ) + cos²(θ) = 1 (Pythagorean identity)
- sin(θ) = cos(90° − θ)
- sin(−θ) = −sin(θ) (odd function)
Common Values:
sin(0°) = 0
sin(30°) = 1/2
sin(45°) = √2/2
sin(60°) = √3/2
sin(90°) = 1
About Sine Calculator
The Sine Calculator calculates sine values for any angle in degrees or radians. Sine is one of the fundamental trigonometric functions used extensively in mathematics, physics, and engineering.
When to Use This Calculator
- Trigonometry Problems: Solve trigonometric equations and identities
- Physics Calculations: Calculate wave motion, oscillations, and forces
- Engineering: Design mechanical systems and analyze signals
- Navigation: Compute distances and positions
- Verification: Double-check manual calculations
Why Use Our Calculator?
- ✅ Instant Results: Get accurate sine values immediately
- ✅ Multiple Units: Supports both degrees and radians
- ✅ Related Values: Shows cosine and tangent for the same angle
- ✅ 100% Free: No registration required
- ✅ Mobile Friendly: Works on all devices
Frequently Asked Questions
What is the difference between degrees and radians?
Degrees measure angles as parts of 360° (full circle), while radians measure as parts of 2π (≈6.28). To convert: radians = degrees × π/180.
Why does sine range from -1 to 1?
On the unit circle (radius = 1), sine represents the y-coordinate, which ranges from -1 (bottom) to +1 (top) as the angle rotates.
What is sin(90°)?
sin(90°) = 1. This is the maximum value of the sine function.
How is sine related to cosine?
sin²(θ) + cos²(θ) = 1 (Pythagorean identity). Also, sin(θ) = cos(90° − θ) (complementary angles).
What are the sine values I should memorize?
Key values: sin(0°)=0, sin(30°)=1/2, sin(45°)=√2/2, sin(60°)=√3/2, sin(90°)=1. These are essential for quick calculations!