🎓 Mathematics • Trigonometry
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Sine Calculator
Computes sine of any angle in degrees or radians with unit circle coordinate representations.
Unit Circle Angles:
Trigonometric Functions & Unit Circle Calculator
Angle = 45° = 0.7854 rad (≈ 0.25π)
Trigonometric Ratios & Unit Circle Coordinates
(cos θ, sin θ) = (0.7071, 0.7071)
Sinesin(θ) = 0.7071Exact: √2/2
Cosinecos(θ) = 0.7071Exact: √2/2
Tangenttan(θ) = 1Exact: 1
Cosecant (1/sin)csc(θ) = 1.4142
Secant (1/cos)sec(θ) = 1.4142
Cotangent (1/tan)cot(θ) = 1
What is the Sine Function?
The sine of an angle is the ratio of the opposite side length to the hypotenuse in a right triangle.
Formula & Step-by-Step Calculation
sin(θ) = y / r
Y-coordinate on a unit circle of radius 1.
Worked Step-by-Step Examples
Example 1
sin(30°)
Solution: 0.5
• sin(30°) = 1/2 = 0.5
Common Real-World & Academic Use Cases
- ✓ Harmonic sound waves
- ✓ Alternating electrical currents
- ✓ Triangulation
How to Use the Sine Calculator
1
Enter Angle
Input angle in deg or rad.
2
View Sine
Inspect exact value.
Frequently Asked Questions
Q: What is the range of sine?
For real angles, sin(θ) always lies between -1 and +1.