Trigonometry Calculator
This trigonometry calculator finds sine, cosine, tangent, and their reciprocals the moment you type an angle. Switch between degrees and radians, and flip to inverse mode to turn a ratio back into an angle with arcsin, arccos, and arctan. You'll see all six functions at once next to a live unit circle that sweeps to your angle and marks the point (cos, sin), so you can watch where the values come from instead of just reading them off.
- All six functions
- Degrees or radians
- Inverse functions
- Live unit circle
- Exact values
Last updated June 18, 2026 Method: unit circle and inverse functions Reviewed by the Calcowa math team
Enter a valid value to see the result.
Show all six functions
sin(30°) = 0.5, cos(30°) = 0.8660, tan(30°) = 0.5774
What are sine, cosine, and tangent?
Sine, cosine, and tangent are the three core trigonometric functions, and they're easier than they look. On a right triangle, sine is the opposite side over the hypotenuse, cosine is the adjacent over the hypotenuse, and tangent is the opposite over the adjacent. The memory trick that'll stick is SOH-CAH-TOA. For a 30° angle, sin is 0.5.
The unit circle's what ties it all together. A point on a circle of radius 1, at angle θ from the positive x-axis, sits at (cosθ, sinθ), so cosine's the x-coordinate and sine's the y-coordinate, and tangent's the slope of the line to that point. The other three functions are reciprocals: cosecant's 1/sin, secant's 1/cos, and cotangent's 1/tan. You won't use those last three as often, but they're handy to have.
How do you calculate a trig function?
To find a trig function by hand you'd reach for a table or the unit circle, but the steps don't change either way. Here's how it goes, and it's quick once you've done it a couple of times:
- 1
Set the angle unitDecide whether your angle is in degrees or radians, since that's easy to mix up.
- 2
Place the angle on the unit circleMeasure the angle counterclockwise from the positive x-axis.
- 3
Read the coordinatesCosine is the x-coordinate of the point, and sine is the y-coordinate.
- 4
Divide for tangentTangent is sine divided by cosine, the slope of the radius line.
- 5
Take reciprocals if neededCosecant, secant, and cotangent are 1/sin, 1/cos, and 1/tan.
Inverse trig functions, explained
The inverse functions run the process in reverse. Where sine turns an angle into a ratio, arcsine turns a ratio back into an angle. So arcsin(0.5) is 30°, because sin 30° is 0.5, and it's the same idea for arccos and arctan. Arcsin and arccos won't take a value outside -1 to 1, since sine and cosine can't go beyond that range, while arctan'll accept anything you give it. Flip the calculator to inverse mode and you'll see it work.
Exact values for common angles
These exact values come from the 30-60-90 and 45-45-90 triangles, and they're the ones worth memorizing. The calculator shows decimals, but if you know the exact forms you'll spot patterns faster and you'll catch your own mistakes. They're the values teachers expect you to recall without a tool.
| Angle | sin | cos | tan |
|---|---|---|---|
| 0° (0) | 0 | 1 | 0 |
| 30° (π/6) | 1/2 | √3/2 | 1/√3 |
| 45° (π/4) | √2/2 | √2/2 | 1 |
| 60° (π/3) | √3/2 | 1/2 | √3 |
| 90° (π/2) | 1 | 0 | undefined |
Frequently asked questions
Does this trigonometry calculator solve triangles too?
This one focuses on the trig functions and the unit circle, so it's built around angles and ratios. If you need to find the sides and angles of a triangle from a couple of measurements, the right triangle calculator is the better fit, and it links from here. Use this tool when you want sine, cosine, tangent, or their inverses for a given angle.
It works out the six trigonometric functions (sine, cosine, tangent, and their reciprocals cosecant, secant, and cotangent) for any angle you enter. You can switch between degrees and radians, and you can also run it in reverse: give it a ratio and it finds the angle with the inverse functions. It's a quick way to check homework or look up a value without a function table.
On a right triangle, sine is the opposite side over the hypotenuse, cosine is the adjacent side over the hypotenuse, and tangent is the opposite over the adjacent. On the unit circle, a point at angle θ sits at (cosθ, sinθ), so cosine is the x-coordinate and sine is the y-coordinate. Tangent is just sin divided by cos.
Sin 30° is exactly 0.5. Cos 30° is √3/2, which is about 0.866, and tan 30° is 1/√3, about 0.577. These come from the 30-60-90 triangle, and they're worth memorizing since they show up constantly. Type 30 into the calculator with degrees selected and you'll see all six functions at once.
Use the degree-radian toggle above the input. One full turn is 360 degrees or 2π radians, so to convert, multiply degrees by π/180 to get radians, or multiply radians by 180/π to get degrees. The calculator handles the conversion for you, so you can work in whichever unit your problem uses.
The inverse functions, arcsin, arccos, and arctan, go the other way: you give them a ratio and they return the angle. For example, arcsin(0.5) is 30° because sin 30° equals 0.5. Switch the calculator to its inverse mode, enter a ratio between -1 and 1 for arcsin or arccos, and it'll give you the angle.
Tangent is undefined at 90° and 270° (and every 180° from there), because cosine is zero at those angles and tangent divides by cosine. You can't divide by zero, so the value shoots off toward infinity. The calculator flags those angles instead of showing a number, which is the honest answer.
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