Trig Ratio Calculator Degrees

This trigonometric ratio calculator computes sine, cosine, and tangent values for any angle in degrees. It provides precise results and visualizes the ratios on a unit circle.

What Are Trigonometric Ratios?

Trigonometric ratios relate the angles of a right triangle to the lengths of its sides. The three primary ratios are:

Sine (sin) - Opposite side divided by hypotenuse
Cosine (cos) - Adjacent side divided by hypotenuse
Tangent (tan) - Opposite side divided by adjacent side

These ratios are fundamental in trigonometry and have applications in physics, engineering, and navigation.

How to Use This Calculator

Enter an angle in degrees (0-360)
Click "Calculate"
View the sine, cosine, and tangent values
See the visualization on the unit circle

Note

The calculator uses the standard trigonometric functions from JavaScript's Math library, which handles all angle ranges correctly.

Formula

Trigonometric Ratios Formula

For an angle θ in degrees:

sin(θ) = opposite/hypotenuse
cos(θ) = adjacent/hypotenuse
tan(θ) = opposite/adjacent

In JavaScript, these are calculated as:

sin = Math.sin(θ * Math.PI / 180)
cos = Math.cos(θ * Math.PI / 180)
tan = Math.tan(θ * Math.PI / 180)

Examples

Angle (degrees)	sin(θ)	cos(θ)	tan(θ)
0°	0	1	0
30°	0.5	0.866	0.577
45°	0.707	0.707	1
60°	0.866	0.5	1.732
90°	1	0	Undefined

FAQ

What is the difference between degrees and radians?

Degrees are a measure of angle where a full circle is 360°. Radians measure angles based on the radius of a circle, with π radians equal to 180°. This calculator works with degrees.

Why is tan(90°) undefined?

At 90°, the adjacent side length becomes zero, making the tangent ratio (opposite/adjacent) undefined. This occurs because the line is vertical and has no horizontal component.

Can I use negative angles?

Yes, the calculator accepts angles from -360° to 360°. Negative angles are measured clockwise from the positive x-axis.