Trig Functions Calculator
Enter one angle and this calculator returns all six trigonometric functions at once: sine, cosine, tangent, cosecant, secant and cotangent. It works in degrees or radians and converts between them, and it flags the genuinely undefined cases, such as tangent at 90 degrees, instead of printing a misleading huge number.
How to find the trig functions of an angle
- Type the angle into the Angle field, or use the stepper arrows to nudge it.
- Click Degrees or Radians to tell the calculator how to read that value.
- Read the line that echoes the angle in both degrees and radians to confirm the unit.
- Check the six result cards: sin and cos are always shown, while tan, csc, sec and cot read 'undefined' where they have no value.
- Click Copy result to copy the angle and all six functions as text.
Examples
A 30 degree angle (all six defined)
angle = 30, unit = degrees
sin 0.5, cos 0.866, tan 0.5774, csc 2, sec 1.1547, cot 1.7321
45 degrees, where sine and cosine match
angle = 45, unit = degrees
sin 0.7071, cos 0.7071, tan 1, csc 1.4142, sec 1.4142, cot 1
90 degrees, where tangent and secant break down
angle = 90, unit = degrees
sin 1, cos 0, tan undefined, csc 1, sec undefined, cot 0
Frequently asked questions
What are the six trigonometric functions?
They are sine, cosine and tangent, plus their reciprocals: cosecant is 1 over sine, secant is 1 over cosine, and cotangent is cosine over sine. This tool reports all six for the angle you enter.
Why is tangent undefined at 90 degrees?
Tangent is sine divided by cosine, and at 90 degrees the cosine is zero, so the division has no result. Secant, which is 1 over cosine, is undefined at the same angle for the same reason.
When are cosecant and cotangent undefined?
Both are built on dividing by sine. At 0 and 180 degrees, and every multiple of 180, the sine is zero, so cosecant and cotangent have no value and are shown as undefined.
Can I enter the angle in radians?
Yes. Click Radians and type a decimal such as 0.5236 for pi over 6. When you use degrees the tool converts internally with radians equal to degrees times pi over 180.
How does the tool decide a value is undefined?
Sine and cosine rarely return an exact zero at right angles because of floating-point rounding, so any magnitude below a tolerance of 1e-12 is treated as zero. The dependent reciprocal is then reported as undefined rather than a meaningless spike.
How are the results rounded?
Defined values are rounded to four decimal places to hide floating-point noise, which is why cos 30 degrees shows as 0.866 and tan 30 as 0.5774. The underlying calculation uses full double precision.
What angle range can I enter?
The field accepts angles from -3600 to 3600, so several full turns in either direction. Negative angles and values beyond one full rotation are handled the same way, since the functions are periodic.
Does it compute inverse functions like arcsin?
No. This tool evaluates the six direct functions of a known angle. To go the other way, from a ratio back to an angle, you need an inverse trig or arcsine style calculator instead.
Is anything sent to a server?
No. Every calculation happens locally in your browser, so the angle you type and the results stay on your device.
Learn more
- Cosecant, secant and cotangent explained
How the three reciprocal trig functions relate to sine, cosine and tangent, when each one is undefined, and how to read them off the unit circle.
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