About the Trigonometry Calculator
Enter an angle and this calculator returns its sine, cosine, tangent, cosecant, secant and cotangent. The angle can be in degrees, radians or gradians. For angles that are multiples of 30 or 45 degrees, it also shows the exact form, such as sin 60° = √3/2. A second mode goes the other way: type a ratio and get the angle from arcsin, arccos, arctan, arccsc, arcsec or arccot, in degrees, radians and gradians. A separate box gives sinh, cosh and tanh. Results use ordinary floating-point arithmetic, shown to ten significant digits, and tiny rounding dust such as 6e-17 is shown as zero. Where a ratio does not exist, for example tan 90°, the page says undefined instead of a huge number. Inverse answers are principal values only.
Updated September 2026
How to use the Trigonometry Calculator
- 1Choose Angle to ratios, then type the angle and pick degrees, radians or gradians. Tap a common angle such as 45° for a quick start.
- 2Read sin, cos and tan, with their reciprocals csc, sec and cot. Exact forms appear beside the special angles.
- 3To find an angle from a ratio, switch to Ratio to angle, pick the function and type the value.
- 4Read the answer in degrees, radians and gradians, and press Copy beside any result.
- 5Use the Hyperbolic functions box for sinh, cosh and tanh of a number.
What the six ratios mean
In a right triangle, the sine of an angle is the opposite side over the hypotenuse, the cosine is the adjacent side over the hypotenuse, and the tangent is opposite over adjacent. Cosecant, secant and cotangent are the reciprocals of sine, cosine and tangent. The same ratios extend to any angle through the unit circle, where cosine is the x-coordinate of a point and sine is its y-coordinate.
That is why the results change sign with the quadrant: sine is positive in the top half of the circle and cosine in the right half.
Degrees, radians and gradians
Choose the unit your problem uses. Mixing them is the most common cause of a wrong answer.
- Degrees: 360 to a full turn, used in school geometry and surveying
- Radians: 2π to a full turn, used in calculus, physics and programming
- Gradians: 400 to a full turn, used in some surveying tools
- A calculator set to degrees gives sin 90 = 1, but in radian mode it gives about 0.894
Working back from a ratio
If you know two sides of a right triangle, divide them to get a ratio and use the matching inverse function to find the angle. For a slope of 0.75, arctan gives about 36.87°. To solve a whole triangle from any three known parts, use the Triangle Calculator, and for the third side of a right triangle the Pythagorean Theorem Calculator is quicker.
To convert angles between units or to degrees, minutes and seconds, use the Angle Converter. For the steepness of a line, the Slope Calculator shows the angle too.
Features
- Six trig ratios for any angle: sin, cos, tan, csc, sec and cot
- Degrees, radians and gradians
- Exact values for multiples of 30° and 45°, such as √2/2
- Inverse functions: arcsin, arccos, arctan, arccsc, arcsec and arccot
- Sinh, cosh and tanh
- Tap-to-fill common angles
- Says undefined where a ratio does not exist, and explains domain errors
- Runs in your browser with nothing sent anywhere
Frequently asked questions
How do I find sin, cos and tan of an angle?
Type the angle, choose degrees or radians and read the rows. For 30° the page shows sin 0.5, cos 0.866025 and tan 0.57735. Make sure the unit is right, because sin 30 in radians is a very different number from sin 30°.
Why does tan 90° say undefined?
Tangent is sine divided by cosine, and cos 90° is zero, so the division has no answer. The graph of tan shoots off to infinity there. The same happens for csc and cot at 0° and 180°, and for sec at 90° and 270°.
How do I switch between degrees and radians?
Pick the unit next to the angle. To convert, multiply degrees by π/180 to get radians. A line under the results shows your angle in both degrees and radians, which helps you check that you entered what you meant.
How do I find an angle from a sine, cosine or tangent value?
Use Ratio to angle and choose arcsin, arccos or arctan. For arcsin of 0.5 you get 30°, which is 0.5236 radians. Sine and cosine only exist between −1 and 1, so the page warns you when the value is outside that range.
What are the exact values it shows?
For 0°, 30°, 45°, 60°, 90° and their equivalents in every quadrant, the exact form is a simple root or fraction, such as cos 30° = √3/2 and tan 60° = √3. They are written from the standard unit circle table, not rounded, and signs follow the quadrant.
Why do I get 0 instead of 1.2e-16 for sin 180°?
Computers store π approximately, so sin(π) comes out as a tiny number like 1.2e-16 instead of zero. The calculator treats anything smaller than one in a trillion as zero, which matches the true answer for angles such as 180° and 360°.
Are the inverse answers the only solution?
No. They are the principal values: arcsin and arctan lie between −90° and 90°, and arccos between 0° and 180°. Other angles share the same ratio, such as 150° and 30° for a sine of 0.5, and you can add any whole number of turns.