Trigonometry Calculator
Calculate sine, cosine, tangent, and their inverse functions (arcsin, arccos, arctan) in degrees or radians — with exact values shown for common angles.
Degrees vs. radians
Degrees divide a full circle into 360 parts and are the more intuitive everyday unit, while radians measure angles based on arc length relative to radius (a full circle equals 2π radians) and are the standard unit used throughout higher mathematics and physics. This calculator handles the conversion automatically based on which unit you select.
A quick reference: 180° equals π radians, 90° equals π/2 radians, and 360° equals 2π radians — useful benchmarks for sanity-checking a conversion.
Forward functions vs. inverse functions
Sin, cos, and tan take an angle as input and return a ratio. Their inverses (arcsine, arccosine, arctangent) do the reverse — they take a ratio and return the angle that would produce it. This is useful whenever you know a ratio (like the slope of a ramp or the ratio of two sides of a triangle) and need to find the corresponding angle.
Inverse trig functions have restricted output ranges by mathematical convention (for example, arcsine only returns values between -90° and 90°) even though the same ratio could technically correspond to other angles — this is a standard convention to keep the inverse functions well-defined. To solve a full triangle's sides and angles at once, use the Triangle Calculator.
Frequently asked questions
Why does arcsine only return angles between -90° and 90°?
This is a mathematical convention to keep the inverse function well-defined — since multiple angles can produce the same sine value, arcsine is restricted to a single consistent range of outputs by definition.
What's a quick way to convert between degrees and radians?
Multiply degrees by π/180 to get radians, or multiply radians by 180/π to get degrees — this calculator handles that conversion automatically based on your selected unit.
What is cos inverse of -1 (arccos -1)?
The arccosine of -1 is 180° (or π radians). This is because cos(180°) = -1, and arccos returns the angle whose cosine equals the input value, in the range [0°, 180°].
What is tan inverse of -1 (arctan -1)?
The arctangent of -1 is -45° (or -π/4 radians). This is because tan(-45°) = -1, and arctan returns angles in the range (-90°, 90°).
When does sin equal -1?
Sin equals -1 at 270° (or -90°, or 3π/2 radians). This is the lowest point on the sine wave, directly below the centre of the unit circle.