Trigonometry Calculator

Enter any angle and pick degrees or radians, and the calculator returns all six trigonometric functions at once: sine, cosine, tangent, and their reciprocals cosecant, secant, and cotangent. Most homework and exam problems only need the first three, but seeing all six together helps you spot relationships like tan = sin / cos.

Angles can be negative or larger than 360 degrees; the functions are periodic, so sin(390°) equals sin(30°). Where a function has no finite value, for example tan(90°), the calculator says undefined instead of printing a misleading huge number.

The single most common trig mistake is mixing up degrees and radians. Typing 30 while the calculator is in radian mode computes sin(30 radians), which is -0.988, not 0.5. School geometry almost always uses degrees; calculus and physics usually use radians, where a full circle is 2π.

Convert between them with a fixed factor: radians = degrees × π / 180. So 30° is π/6 ≈ 0.5236 rad, 45° is π/4 ≈ 0.7854 rad, and 90° is π/2 ≈ 1.5708 rad. If your answer looks nothing like the triangle you sketched, the unit setting is the first thing to check.

Inverse mode works backwards: give it a ratio and it returns the angle. Enter 0.5 with arcsin and you get 30° (0.5236 rad), because sin(30°) = 0.5. This is the step students miss when a problem gives side lengths and asks for an angle.

Arcsin and arccos only accept inputs from -1 to 1, since no sine or cosine value can fall outside that range; the calculator rejects anything else with a clear message. Arctan accepts any real number. Inverse functions return the principal value, the standard single answer in the accepted range, so arctan(1) gives 45°, not 225°.

For the angles 0°, 30°, 45°, 60°, and 90°, the trig values have clean exact forms with square roots, and teachers love testing them. Memorizing the pattern saves time: sine goes 0, 1/2, √2/2, √3/2, 1 across those five angles, and cosine runs the same list backwards.

When your angle matches one of these, the calculator shows the exact form next to the decimal, so you can give the answer your teacher expects. Decimal approximations are fine for applied problems, but exact forms keep full precision through multi-step solutions.

Every trig ratio comes from a right triangle: SOH-CAH-TOA stands for Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent. Pick the ratio that uses the sides you know and the one you want.

Example: a 10-meter ladder leaning so it makes 60° with the ground reaches 10 × sin(60°) ≈ 8.66 meters up the wall. The adjacent side touches the angle (but is not the hypotenuse); the opposite side faces it. Label the triangle before you calculate and the right ratio picks itself.

This tool covers trig values and inverse trig, which is the whole trig workload for most classes. When a problem mixes trig with logarithms, exponents, factorials, or complex expressions, switch to the scientific calculator instead of chaining tools.

For pure root and power work without any trig, the square root calculator handles square, cube, and nth roots with simplified radicals, which pairs well with the exact-value table above.