Trigonometry Calculator: Sin, Cos, Tan and Inver...

Trigonometric Functions

Trigonometry relates angles of triangles to the ratios of their sides. The six trigonometric functions (sine, cosine, tangent, and their reciprocals) describe these relationships and extend to all real numbers via the unit circle. They appear throughout physics, engineering, signal processing, and computer graphics.

📐 Trigonometry Calculator

Free calculator for instant results.

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📐 Formula

sin(θ)=O/H | cos(θ)=A/H | tan(θ)=O/A

O=opposite, A=adjacent, H=hypotenuse. SOHCAHTOA mnemonic. Reciprocals: csc=1/sin, sec=1/cos, cot=1/tan. Pythagorean identity: sin²θ+cos²θ=1.

📝 Worked Example

θ = 30°:
sin(30°) = 0.5, cos(30°) = √3/2 ≈ 0.866, tan(30°) = 1/√3 ≈ 0.577
Triangle: opp=5, hyp=10 → sin(θ)=0.5 → θ=30°

📝 How to Use

Enter AngleDegrees or radians — toggle between them.

Calculate FunctionsView all six trig values and their exact forms where applicable.

Inverse FunctionsEnter sin/cos/tan value to find the angle (arcsin, arccos, arctan).

Solve TriangleEnter sides/angles to solve the entire triangle via sine or cosine rule.

❓ FAQ

What is the difference between degrees and radians?

Both measure angles. Degrees divide a circle into 360 parts. Radians use arc length: 2π radians = 360°. Scientific functions default to radians.

What is the unit circle?

A circle of radius 1 centered at origin. The coordinates of a point at angle θ are (cos θ, sin θ). Defines trig functions for all angles, not just 0–90°.

Trigonometric Functions