Trigonometry Calculator
Enter an angle above.
Right Triangle Solver
Enter any two values (at least one side). Angles in degrees.
Not enough information or conflicting values.
Trigonometric Functions Explained
Trigonometry deals with the relationships between angles and sides of triangles. The six fundamental trig functions — sine, cosine, tangent and their reciprocals — are used across mathematics, physics, engineering, and computer graphics.
SOHCAHTOA Memory Aid
- SOH – Sin = Opposite / Hypotenuse
- CAH – Cos = Adjacent / Hypotenuse
- TOA – Tan = Opposite / Adjacent
Common Trig Values
| Angle | sin | cos | tan |
|---|---|---|---|
| 0° | 0 | 1 | 0 |
| 30° | 1/2 | √3/2 | 1/√3 |
| 45° | √2/2 | √2/2 | 1 |
| 60° | √3/2 | 1/2 | √3 |
| 90° | 1 | 0 | undefined |
Frequently Asked Questions
What is the difference between sin and arcsin?
sin(θ) takes an angle and returns a ratio. arcsin (inverse sine) takes a ratio and returns the angle. They are inverse operations of each other.
Why is tan(90°) undefined?
tan(θ) = sin(θ)/cos(θ). At 90°, cos(90°) = 0, and division by zero is undefined. The function approaches ±infinity as θ approaches 90°.
Where is trigonometry used in real life?
Architecture (roof angles), navigation (bearing and distance), physics (wave functions, oscillation), computer graphics (rotation matrices), music (Fourier analysis of sound waves), and astronomy (measuring distances to stars).