How to calculate trigonometric functions
Choose the correct direction
Use sin, cos or tan when you know an angle and need a ratio. Choose degrees or radians for that angle. Use asin, acos or atan when you know a ratio and need the principal angle; the unit selector then controls the angle output.
Enter decimal numbers with a period and select Calculate. Editing any field clears the confirmed result so a copied value cannot silently refer to older input.
Definitions and principal ranges
On the unit circle, sin θ is the vertical coordinate and cos θ is the horizontal coordinate; tan θ = sin θ / cos θ. In a right triangle they are opposite/hypotenuse, adjacent/hypotenuse and opposite/adjacent.
asin returns an angle from −90° to 90°, acos from 0° to 180°, and atan from −90° to 90° (endpoints excluded for atan). In radians these are −π/2 to π/2, 0 to π, and −π/2 to π/2.
Domains, undefined values and precision
asin and acos require a ratio between −1 and 1. atan accepts any finite ratio. Tangent is not finite where cosine is zero, such as 90° plus whole multiples of 180°; the calculator reports that condition instead of displaying a huge misleading number.
Ordinary values display with at most two decimal places. Meaningful very small nonzero values use significant digits; exact-looking special angles are cleaned near zero.
Worked examples
Direct functions
sin(30°) = 0.5, cos(π rad) = −1, and tan(45°) = 1. For tan(90°), no finite result exists.
Inverse functions
asin(0.5) = 30° or about 0.52 rad. acos(−1) = 180°, while atan(1) = 45°.
Frequently asked questions
Is sin⁻¹ the same as 1/sin?
No. Here sin⁻¹ means inverse sine (asin). The reciprocal of sine is cosecant.
Why can different angles have the same sine?
Trigonometric functions are periodic. An inverse function must choose one principal angle.
Should I use degrees or radians?
Use the unit in your problem. A full turn is 360° or 2π radians.
Why is tan(90°) rejected?
Because cos(90°) is zero, so sin θ / cos θ has no finite value.