Trigonometry Calculator — sin, cos, tan & Inverse Trig
Calculate all 6 trigonometric functions (sin, cos, tan, csc, sec, cot) for any angle in degrees or radians. Also supports inverse trig functions.
Special angles:
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sin
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cos
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tan
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csc (1/sin)
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sec (1/cos)
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cot (1/tan)
Unit Circle Position
Trigonometric Values Table
| Angle | Radians | sin | cos | tan |
|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 0 |
| 30° | π/6 | 1/2 | √3/2 | 1/√3 |
| 45° | π/4 | √2/2 | √2/2 | 1 |
| 60° | π/3 | √3/2 | 1/2 | √3 |
| 90° | π/2 | 1 | 0 | undefined |
| 180° | π | 0 | -1 | 0 |
| 270° | 3π/2 | -1 | 0 | undefined |
| 360° | 2π | 0 | 1 | 0 |
Frequently Asked Questions
What are the six trigonometric functions?
The six trig functions are: sin (sine), cos (cosine), tan (tangent), csc (cosecant = 1/sin), sec (secant = 1/cos), and cot (cotangent = 1/tan). They describe ratios between sides of a right triangle or coordinates on a unit circle.
What is the difference between degrees and radians?
360 degrees = 2π radians. To convert: degrees × π/180 = radians; radians × 180/π = degrees. Mathematicians typically use radians (more natural in calculus), while engineers often use degrees.
What are the special angle values?
Key values: sin(0°)=0, sin(30°)=0.5, sin(45°)=√2/2≈0.707, sin(60°)=√3/2≈0.866, sin(90°)=1. Cosine follows the reverse pattern. Tan(45°)=1, tan(90°) is undefined.
What are inverse trig functions?
Inverse trig functions (arcsin, arccos, arctan) find the angle given a ratio. arcsin(0.5) = 30°, arccos(0.5) = 60°, arctan(1) = 45°. They have restricted domains: arcsin and arccos take values in [-1, 1]; arctan takes any real number.
What is the unit circle?
The unit circle is a circle with radius 1 centered at the origin. For any angle θ, the point (cos θ, sin θ) lies on the unit circle. It provides a visual way to understand all trigonometric values for any angle.