Trigonometry links angles to side ratios in right triangles.
About this calculator
Trigonometry links angles to side ratios in right triangles. This calculator evaluates sin, cos, and tan for any angle in degrees, plus the inverse functions when you know the ratio and need the angle back.
Enter 30 for sin and you get 0.5 — the classic half-unit opposite a 30° angle on the unit circle. Switch to arctan and input 1 to recover 45°.
Angles stay in degrees because that is what most school papers and site surveys use. For triangle side lengths from two sides, try the [[pythagorean]] calculator. For slope between two points use the [[slope]] calculator. For general arithmetic use the [[math-calculator]].
Common uses
- Evaluate sin/cos/tan for board exam triangle problems
- Convert a slope ratio back to an angle with arctan
- Check engineering sketches that specify degrees
- Verify inverse trig inputs stay within −1 to 1
Frequently asked questions
What is sin 30°?
0.5. In a 30-60-90 triangle the side opposite 30° is half the hypotenuse, so sin 30° = 1/2.
Why must arcsin input be between −1 and 1?
Sine values on the unit circle never exceed 1 or go below −1. Ratios outside that range have no real inverse sine.
Are angles in degrees or radians here?
Degrees. Multiply by π/180 internally. For radian-based tools use a scientific calculator mode or convert first.
What is tan 45°?
1. At 45° the opposite and adjacent legs are equal, so tan = opposite/adjacent = 1.