Overview
There are three basic trigonometric functions: sine, cosine and tangent. Each relates an angle in a right triangle to a ratio of two sides, and they extend to the unit circle to cover all positive and negative angles.
Formula
sin θ = opposite ÷ hypotenuse, cos θ = adjacent ÷ hypotenuse, tan θ = sin θ ÷ cos θ.
How it works
Enter the angle
Choose degrees or radians.
Convert to radians
The calculator works in radians internally.
Compute the ratios
Evaluate sin, cos and tan.
Read reciprocal values
sec, csc and cot are also shown.
Worked examples
Example 1: angle 30°
sin 30° = 0.5, cos 30° ≈ 0.8660, tan 30° ≈ 0.5774.
Example 2: angle 45°
sin 45° = cos 45° ≈ 0.7071, tan 45° = 1.
Frequently asked questions
What is the difference between degrees and radians?
A full turn is 360 degrees or 2π radians; radians are the natural unit in calculus.
Why is tan 90° undefined?
Because cos 90° = 0, and tangent is sine divided by cosine.
Can the ratios be negative?
Yes, in the second, third and fourth quadrants of the unit circle.
This calculator is for educational and informational purposes only and is not a substitute for professional advice.