Why does arcsin only give one answer?

An inverse function must return a single output, so arcsin is restricted to a principal range of −90° to 90°. Other angles with the same sine exist, such as 150° for a sine of 0.5. To find all of them, use the symmetry of the unit circle and add multiples of 360°.

When do I use the law of sines instead of SOH CAH TOA?

SOH CAH TOA only applies to right triangles. For triangles without a right angle, use the law of sines when you know an angle and its opposite side, and the law of cosines when you know two sides and the angle between them or all three sides.

Why is tan 90° undefined?

Tangent equals sine divided by cosine, and cos 90° is 0. Division by zero has no value, so the tangent grows without bound as the angle approaches 90° and is undefined at exactly 90°.

Trigonometry calculators

Q: Why does my calculator give a strange value for sin(30)?

It is almost certainly in radian mode. In degrees, sin(30) is exactly 0.5; interpreted as 30 radians, the result is about −0.988. Switch the angle mode or convert the angle first.

These tools cover the six trig functions and their inverses, exact unit circle values, solving right triangles, solving trig equations over an interval, and converting between degrees and radians. They are the building blocks for problems involving angles, slopes, waves and rotations.

5 tools · Updated October 21, 2026

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sin⁻¹Inverse Trig CalculatorFunctions, values and angle unitsarcsin(0.5) in degrees30° = π/6 rad

a²+b²Right Triangle SolverTriangles and equationsRight triangle with legs 3 and 4c = 5, A = 36.8699°

θTrigonometric Equation SolverTriangles and equations2sin(x) − 1 = 0, 0 ≤ x < 2πx = π/6, 5π/6

sinTrigonometry CalculatorFunctions, values and angle unitssin 30°0.5 (exact 1/2)

θUnit Circle CalculatorFunctions, values and angle unitsPoint at 150° on the unit circle(−√3/2, 1/2)

Which one do I need?

I want sin, cos or tan of an angleTrigonometry Calculator I know a ratio and want the angle (arcsin, arccos or arctan)Inverse Trig Calculator I know a side and an angle of a right triangle and need the restRight Triangle Solver I need exact values like √3/2 for standard anglesUnit Circle Calculator I need every solution of an equation like 2 sin x = 1 in a rangeTrigonometric Equation Solver

SOH CAH TOA and the unit circle

In a right triangle, sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent. The Right Triangle Solver applies these ratios, plus the Pythagorean theorem, to find missing sides and angles from any two known values (at least one of them a side).

The unit circle extends the same functions to every angle. For an angle measured from the positive x-axis, cosine is the x-coordinate and sine is the y-coordinate of the point on a circle of radius 1. That is why sine and cosine are negative in some quadrants, and why the Unit Circle Calculator can give exact values such as √2/2 for 45° instead of rounded decimals.

Inverse functions and multiple solutions

An inverse trig function returns one angle, called the principal value: arcsin and arctan give results between −90° and 90°, and arccos gives results between 0° and 180°. But an equation such as sin x = 0.5 has infinitely many solutions, because sine repeats every 360°.

Use the Inverse Trig Calculator when you only need the principal angle, for example a ramp angle from its rise and run. Use the Trigonometric Equation Solver when you need every solution in an interval such as 0 to 2π, which is what most exam questions ask for.

Degrees, radians and when each is used

A radian is the angle that cuts off an arc equal to the radius, so a full turn is 2π radians, or 360°. Degrees are convenient for navigation, construction and everyday angles. Radians are the natural unit in calculus and physics because they make formulas such as the derivative of sin x equal to cos x hold without extra constants.

The Radians to Degrees Converter handles conversions in either direction and can show results as multiples of π, which is how radian answers are usually written in coursework.

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