What is the difference between sine, cosine, and tangent?

In a right triangle, sine is the ratio of the opposite side to the hypotenuse, cosine is the adjacent side over the hypotenuse, and tangent is the opposite side over the adjacent side.

Should I use degrees or radians?

Degrees are standard in school-level geometry and everyday use. Radians are preferred in calculus, physics, and programming because they simplify many formulas. The tool accepts both and converts automatically.

Why is tan(90°) undefined?

Tangent equals sine divided by cosine. At 90 degrees, cosine equals zero, which creates a division-by-zero condition, making the result undefined.

What are inverse trig functions used for?

Inverse functions find the angle when you know the trigonometric ratio. For example, arcsin(0.5) returns 30 degrees, telling you which angle produces a sine of 0.5.

Can I enter fractions like π/6 or expressions like sqrt(2)/2?

Yes. The calculator parses common mathematical expressions, including pi-based fractions and decimal values, and handles them with full numerical precision.

Why do I sometimes see a tiny non-zero result for sin(180°)?

This is a floating-point rounding artifact. The true value is zero, but 64-bit binary arithmetic introduces extremely small errors for certain angles. The tool displays these within expected precision limits.

How does the right-triangle solver work if I enter just two sides?

The solver applies the Pythagorean theorem to find the third side, then uses arctan or arcsin to calculate both non-right angles and completes the full triangle.

Trigonometry calculator — Free Online

Angle / Value (x)

Unit

x = 45° = 0.785398 rad = 50 grad

sin(x)

0.70710678

cos(x)

0.70710678

tan(x)

cot(x)

sec(x)

1.41421356

csc(x)

1.41421356

asin(x)

—

acos(x)

—

atan(x)

1.54857776 (88.72697 deg)

sinh(x)

17467135528742547456

cosh(x)

17467135528742547456

tanh(x)

asinh(x)

4.4999331 (257.827175 deg)

acosh(x)

4.49968619 (257.813028 deg)

atanh(x)

—

■ sin ■ cos ■ r

📋 Reference — Common angles

°	rad	sin	cos	tan
0°	0	0	1	0
30°	0.5236	1/2	√3/2	1/√3
45°	0.7854	√2/2	√2/2	1
60°	1.0472	√3/2	1/2	√3
90°	1.5708	1	0	∞
180°	3.1416	0	−1	0
270°	4.7124	−1	0	−∞
360°	6.2832	0	1	0

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Trigonometry Calculator

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