Trigonometry Calculator
Calculate trigonometric functions, convert between degrees and radians, and visualize the unit circle
sin(θ) = 0.00
cos(θ) = 0.00
tan(θ) = 0.00
csc(θ) = inf
sec(θ) = 1.00
cot(θ) = inf
Common Trigonometric Values
| Angle (Degrees) | Angle (Radians) | sin(θ) | cos(θ) | tan(θ) | csc(θ) | sec(θ) | cot(θ) |
|---|---|---|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 0 | ∞ | 1 | ∞ |
| 30° | π/6 | 0.5 | 0.866 | 0.577 | 2 | 1.155 | 1.732 |
| 45° | π/4 | 0.707 | 0.707 | 1 | 1.414 | 1.414 | 1 |
| 60° | π/3 | 0.866 | 0.5 | 1.732 | 1.155 | 2 | 0.577 |
| 90° | π/2 | 1 | 0 | ∞ | 1 | ∞ | 0 |
| 120° | 2π/3 | 0.866 | -0.5 | -1.732 | 1.155 | -2 | -0.577 |
| 135° | 3π/4 | 0.707 | -0.707 | -1 | 1.414 | -1.414 | -1 |
| 150° | 5π/6 | 0.5 | -0.866 | -0.577 | 2 | -1.155 | -1.732 |
| 180° | π | 0 | -1 | 0 | ∞ | -1 | ∞ |
| 270° | 3π/2 | -1 | 0 | ∞ | -1 | ∞ | 0 |
| 360° | 2π | 0 | 1 | 0 | ∞ | 1 | ∞ |
Understanding Trigonometry
Trigonometry is a branch of mathematics that studies the relationships between the sides and angles of triangles. It has extensive applications in various fields including physics, engineering, astronomy, architecture, and more.
Basic Trigonometric Functions
The six basic trigonometric functions are sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). These functions relate the angles of a triangle to the lengths of its sides.
The Unit Circle
The unit circle is a circle with a radius of 1 unit centered at the origin of a coordinate system. It is a fundamental tool in trigonometry that helps visualize and understand trigonometric functions. On the unit circle, the coordinates of any point (x, y) correspond to (cos θ, sin θ), where θ is the angle formed by the positive x-axis and the line from the origin to the point.
Applications of Trigonometry
Trigonometry has numerous real-world applications. It is used in navigation to determine distances and directions, in physics to analyze periodic phenomena like waves and oscillations, in engineering to design structures and machines, in astronomy to calculate distances to stars and planets, and in many other fields.