Sin Cos Tan Calculator
Calculate sine, cosine, and tangent values for any angle in a right triangle. Understand trigonometric ratios with our easy-to-use tool and visual explanations based on the SOHCAHTOA principle.
SOHCAHTOA
- SOH: Sin(θ) = Opposite / Hypotenuse
- CAH: Cos(θ) = Adjacent / Hypotenuse
- TOA: Tan(θ) = Opposite / Adjacent
Trigonometric Ratios
| Function | Ratio | Value |
|---|---|---|
| Sine (sin) | Opposite/Hypotenuse | 0.707 |
| Cosine (cos) | Adjacent/Hypotenuse | 0.707 |
| Tangent (tan) | Opposite/Adjacent | 1.000 |
Unit Circle Values
On the unit circle (radius = 1):
- sin(θ) = y-coordinate
- cos(θ) = x-coordinate
- tan(θ) = y-coordinate / x-coordinate
Understanding Sine, Cosine and Tangent
The three main trigonometric functions - sine (sin), cosine (cos), and tangent (tan) - are fundamental in right triangle trigonometry. They relate the angles of a triangle to the lengths of its sides.
Right Triangle Trigonometry
In a right-angled triangle:
- The hypotenuse is the longest side, opposite the right angle
- The opposite side is the side opposite to the angle we're interested in (θ)
- The adjacent side is the side next to angle θ that is not the hypotenuse
Key Properties
These trigonometric functions have important properties:
- sin²θ + cos²θ = 1 (Pythagorean identity)
- tanθ = sinθ / cosθ
- sin(90°-θ) = cosθ and cos(90°-θ) = sinθ
- Values repeat every 360° (periodicity)
Common Angles
Memorizing these common angle values can be helpful:
| Angle (θ) | sin(θ) | cos(θ) | tan(θ) |
|---|---|---|---|
| 0° | 0 | 1 | 0 |
| 30° | 1/2 | √3/2 | √3/3 |
| 45° | √2/2 | √2/2 | 1 |
| 60° | √3/2 | 1/2 | √3 |
| 90° | 1 | 0 | ∞ |
Applications
Trigonometric functions are used in:
Physics
Wave motion, circular motion, alternating current circuits, and projectile motion calculations.
Engineering
Structural analysis, electrical engineering, mechanical design, and signal processing.
Navigation
GPS systems, aviation, maritime navigation, and astronomy calculations.