Trig Calculator
This trigonometry calculator takes a single angle and returns all six trigonometric functions at once: sine, cosine and tangent, together with their reciprocals cosecant, secant and cotangent. Trigonometry links the angles of a triangle to the ratios of its sides, and these functions are the backbone of geometry, surveying, navigation, physics, engineering and computer graphics, as well as a core topic in secondary and tertiary maths. You enter the angle and choose whether it is measured in degrees or radians, and the calculator converts internally and evaluates each function. Degrees are the familiar unit for everyday angles and a full turn is 360 of them, while radians are the natural unit used in calculus, where a full turn is two pi. Some functions are undefined at particular angles, because tangent and secant divide by cosine, which is zero at 90 and 270 degrees, and cosecant and cotangent divide by sine, which is zero at 0 and 180 degrees. The calculator reports undefined in those cases rather than showing a meaningless huge number, and it cleans up the tiny rounding errors that floating point arithmetic can introduce near those points. Enter any angle to see the full set of values update as you type.
How it works
The calculator converts the angle to radians if needed, then evaluates sine and cosine. Tangent is sine divided by cosine. The reciprocals are one over sine for cosecant, one over cosine for secant, and one over tangent for cotangent. Where a denominator is effectively zero, the result is reported as undefined.
Worked example
At 30 degrees, sine is 0.5 and cosine is about 0.8660. Tangent is 0.5 divided by 0.8660, which is about 0.5774. The reciprocals follow: cosecant is 2, secant about 1.1547, and cotangent about 1.7321.
Who this calculator is for
This calculator is for students and anyone computing trigonometric functions such as sine, cosine and tangent, and their inverses.
What this calculator assumes
- The angle and the unit (degrees or radians) you select.
- Standard trigonometric definitions.
- Results are rounded for display.
- Inverse functions return principal values within their standard ranges.
Related calculators
- Sine Cosine Tangent Calculator: the three main ratios.
- Hypotenuse Calculator: right triangle sides.
- Degrees to Radians Calculator: angle units.
- Right Angle Triangle Calculator: solve triangles.