All six trig functions at once
Enter any angle in degrees or radians and this calculator returns all six trigonometric functions -- sine, cosine, tangent, and their reciprocals cosecant, secant, and cotangent. Values that do not exist, like the tangent of 90 degrees, are flagged as undefined rather than shown as a misleading huge number.
What the functions mean
For an angle, sine and cosine are the vertical and horizontal coordinates of the matching point on the unit circle. Tangent is sine over cosine. The reciprocals follow: cosecant is 1 over sine, secant is 1 over cosine, and cotangent is cosine over sine.
Where they are undefined
Tangent and secant are undefined wherever cosine is zero (90, 270 degrees), and cosecant and cotangent are undefined wherever sine is zero (0, 180 degrees). At those angles the reciprocal would divide by zero.
Related tools
To switch the angle between degrees and radians, use the angle converter calculator; to apply these ratios to a triangle, the right triangle calculator.
Worked example
At 30 degrees: sine is 0.5, cosine is about 0.8660, and tangent is about 0.5774, so cosecant is 2, secant about 1.1547, and cotangent about 1.7321.
FAQ
Degrees or radians?
Both are supported -- pick the unit that matches your problem. A full circle is 360 degrees or 2 pi radians.
Why is tan 90 undefined rather than infinite?
Cosine is exactly zero there, so the ratio sine over cosine has no finite value; it grows without bound as you approach 90 from either side.