How to Calculate Trig Functions
What is Trig Functions?
Trigonometric functions (sin, cos, tan, csc, sec, cot) relate the angles and sides of triangles. They extend to the unit circle for all angles and are fundamental in physics, engineering, navigation, signal processing, and wave analysis.
Step-by-Step Guide
- 1In a right triangle: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent
- 2Mnemonic: SOH-CAH-TOA
- 3Unit circle definition: sin θ = y-coordinate, cos θ = x-coordinate, at angle θ from positive x-axis
- 4Reciprocals: csc = 1/sin, sec = 1/cos, cot = 1/tan
Worked Examples
Input
sin 30°
Result
0.5
sin(π/6) = 1/2
Input
cos 60°
Result
0.5
cos(π/3) = 1/2
Input
tan 45°
Result
1
tan(π/4) = sin/cos = 1
Ready to calculate? Try the free Trig Functions Calculator
Try it yourself →