Calculate Sine in Degrees

Calculating sine in degrees is essential in trigonometry, physics, and engineering. This guide explains how to compute sine values, provides a calculator, and includes a reference table of common sine values.

What is Sine?

Sine is a fundamental trigonometric function that relates the angle of a right triangle to the ratio of the length of the opposite side to the hypotenuse. In the unit circle, sine represents the y-coordinate of a point corresponding to a given angle.

The sine function is periodic with a period of 360 degrees, meaning sin(θ) = sin(θ + 360°n) for any integer n. It's an odd function, meaning sin(-θ) = -sin(θ).

Sine Formula

For a right triangle with angle θ, opposite side a, and hypotenuse c:

sin(θ) = opposite / hypotenuse = a / c

In the unit circle, for any angle θ:

sin(θ) = y-coordinate of the point on the unit circle

Important Notes

All angles must be in degrees for this calculator
Results are accurate to 10 decimal places
For angles outside 0-360°, the calculator normalizes them

How to Calculate Sine

Step-by-Step Calculation

Identify the angle in degrees you want to calculate the sine for
Use the sine formula: sin(θ) = opposite/hypotenuse
For angles beyond 360°, subtract 360° until you get an equivalent angle between 0° and 360°
Use the calculator below to verify your result

Example Calculation

Let's calculate sin(30°):

30° is within 0-360°, so no normalization needed
In a 30-60-90 triangle, the opposite side to 30° is 1, and the hypotenuse is 2
sin(30°) = 1/2 = 0.5

Sine Values Table

Here's a table of common sine values for standard angles:

Angle (degrees)	Sine Value
0°	0
30°	0.5
45°	≈0.7071
60°	≈0.8660
90°	1
180°	0
270°	-1
360°	0

Common Sine Questions

What is the range of the sine function?: The sine function ranges from -1 to 1 for all real numbers.
How do I calculate sine for angles greater than 360°?: Subtract 360° repeatedly until you get an angle between 0° and 360°, then calculate the sine of that angle.
What's the difference between sine and cosine?: Sine relates to the y-coordinate in the unit circle, while cosine relates to the x-coordinate. They are co-functions with a 90° phase difference.
Can sine be negative?: Yes, sine is negative in the third and fourth quadrants of the unit circle (180°-360°).
How precise are the sine calculations?: This calculator provides results accurate to 10 decimal places using JavaScript's built-in Math.sin() function.