Trigonometry calculator.
Find the trig functions of any angle. Enter an angle in degrees or radians and the calculator returns sine, cosine, tangent and the reciprocal functions.
Angle
LiveEnter the angle and choose degrees or radians. Tangent and the reciprocal functions are undefined where their denominator is zero, such as tan at 90 degrees.
sin
0.70711
sine of the angle
Standard floating-point trig functions, accurate to several decimal places. Calculations run in your browser; nothing you enter is stored.
How it works
Ratios of an angle
The three core trigonometric functions, sine, cosine and tangent, link an angle to the ratios of sides in a right triangle: sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent, the classic SOH CAH TOA.
The reciprocal functions follow directly: secant is one over cosine, cosecant is one over sine, and cotangent is one over tangent. The calculator evaluates all six for the angle you enter.
Reference
Common angles.
Sine, cosine and tangent for the angles you meet most often.
| Angle | sin, cos, tan |
|---|---|
| 0 deg | 0, 1, 0 |
| 30 deg | 0.5, 0.866, 0.577 |
| 45 deg | 0.707, 0.707, 1 |
| 60 deg | 0.866, 0.5, 1.732 |
| 90 deg | 1, 0, undefined |
The full guide
The complete guide to trigonometric functions.
What sin, cos and tan mean, how degrees and radians relate, and where the functions break.
Sine, cosine and tangent
In a right triangle, sine, cosine and tangent are ratios of side lengths for a given angle. On the unit circle they generalise to any angle: the cosine is the x-coordinate and the sine is the y-coordinate of the point at that angle, and the tangent is their ratio.
SOH CAH TOA is the memory aid: Sine Opposite Hypotenuse, Cosine Adjacent Hypotenuse, Tangent Opposite Adjacent.
Degrees versus radians
A full turn is 360 degrees or 2 pi radians, so one radian is about 57.3 degrees. Radians are the natural unit in calculus and most programming, while degrees are common in everyday geometry. This calculator accepts either.
To convert, multiply degrees by pi over 180 to get radians, or radians by 180 over pi to get degrees.
The reciprocal functions
Secant, cosecant and cotangent are simply the reciprocals of cosine, sine and tangent. They show up often in calculus and physics. Because they invert another function, they are undefined wherever that function is zero.
For example cosecant is undefined at 0 degrees because sine is zero there.
Where the functions are undefined
Tangent and secant are undefined at 90 degrees and 270 degrees, where cosine is zero, and the calculator marks these as undefined rather than showing a huge number. Cosecant and cotangent are undefined at 0 and 180 degrees, where sine is zero.
These gaps are the vertical asymptotes you see on the graphs of those functions.
The formula
SOH CAH
TOA.
Sine, cosine and tangent are ratios of a right triangle’s sides; secant, cosecant and cotangent are their reciprocals.
Circumference calculator ›# Trig functions
radians = degrees × pi / 180
sin, cos, tan of the angle
sec = 1/cos, csc = 1/sin, cot = 1/tan
# 45 deg
sin = cos = 0.70711, tan = 1Questions
Trigonometry questions.
How do I find sin, cos and tan of an angle?
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Enter the angle and choose degrees or radians. The calculator returns the sine, cosine and tangent, plus the reciprocal functions sec, csc and cot.
How do I convert degrees to radians?
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Multiply the angle in degrees by pi divided by 180. The calculator does this for you when you pick degrees, since the underlying functions work in radians.
Why is tan 90 degrees undefined?
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Because tangent is sine over cosine, and cosine is zero at 90 degrees. Dividing by zero is undefined, which is why the graph of tangent has a vertical asymptote there.
What are sec, csc and cot?
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They are the reciprocal functions: secant is one over cosine, cosecant is one over sine, and cotangent is one over tangent. They are undefined wherever the base function is zero.
Is this trigonometry calculator free?
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Yes. It is completely free with no sign-up, and every calculation runs locally in your browser, so nothing you enter is stored or sent anywhere.
About the developer
Jean Borg
Jean builds and maintains every calculator on freecalculators.pro from Malta, with a focus on tools that are fast, free and show their working. The trigonometry calculator evaluates all six trig functions for an angle in degrees or radians.