Sine Table in Degrees Calculator

The sine table in degrees calculator provides precise sine values for any angle between 0° and 360°. This tool is essential for trigonometry, physics, engineering, and navigation where understanding the sine function is crucial.

What is Sine?

Sine is a 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 corresponds to the y-coordinate of a point at a given angle from the origin.

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

Sine values range between -1 and 1 for all real numbers. Common sine values include sin(0°) = 0, sin(30°) ≈ 0.5, sin(45°) ≈ 0.707, sin(60°) ≈ 0.866, and sin(90°) = 1.

Sine Table

A sine table provides sine values for common angles. Here's a partial table for reference:

Angle (°)	Sine Value
0°	0
30°	0.5
45°	≈0.707
60°	≈0.866
90°	1
180°	0
270°	-1
360°	0

This table shows that sine values repeat every 360° and are symmetric about the origin.

How to Use This Calculator

Enter the angle in degrees in the input field.
Click the "Calculate" button to compute the sine value.
View the result in the result panel below.
Use the "Reset" button to clear the form.

The calculator accepts angles between 0° and 360° and provides results with up to 6 decimal places.

Formula

The sine of an angle θ in degrees is calculated using the following formula:

sin(θ) = opposite / hypotenuse

In the unit circle, sin(θ) = y-coordinate of the point at angle θ.

For angles outside 0°-360°, the calculator normalizes the angle by subtracting multiples of 360° until it falls within this range.

Example Calculation

Let's calculate sin(120°):

120° is in the second quadrant where sine is positive.
Reference angle = 180° - 120° = 60°.
sin(120°) = sin(60°) = 0.866 (from the sine table).

The calculator would return 0.866025 for sin(120°).

FAQ

What is the range of sine values?: Sine values range from -1 to 1 for all real numbers.
How do I calculate sine for angles outside 0°-360°?: The calculator normalizes angles by subtracting multiples of 360° until the angle falls within 0°-360°.
What is the sine of 90°?: The sine of 90° is exactly 1.
How accurate are the sine values calculated?: The calculator provides results with up to 6 decimal places of precision.
Can I use this calculator for negative angles?: Yes, the calculator accepts negative angles and computes their sine values correctly.