How do degrees and radians compare in trigonometry?

A complete circle is 360 degrees, which equals 2*pi radians (approx 6.28318 rad). To convert degrees to radians, multiply by (pi / 180). To convert radians to degrees, multiply by (180 / pi).

What are reciprocal trigonometric functions?

The reciprocals are Cosecant (csc = 1/sin), Secant (sec = 1/cos), and Cotangent (cot = 1/tan).

When does tan(x) become undefined?

Tangent equals sin(x) / cos(x). Whenever cos(x) = 0 (at 90 degrees, 270 degrees, pi/2, 3pi/2, etc.), division by zero occurs, making tan(x) undefined.

Is this trigonometry calculator free?

Yes, 100% free with instant precision results.

Trigonometry Calculator - Sin, Cos, Tan in Degrees & Radians

What are Trigonometric Functions?

Trigonometric functions relate the angles of a right triangle to the ratios of its side lengths. The primary functions are Sine ($sin = ext{Opposite}/ ext{Hypotenuse}$), Cosine ($cos = ext{Adjacent}/ ext{Hypotenuse}$), and Tangent ($ an = ext{Opposite}/ ext{Adjacent}$). Beyond right triangles, trigonometry describes periodic continuous waveforms essential to sound design, electrical AC power grids, orbital mechanics, and computer game graphics.

Key Capabilities

Degree & Radian Dual Mode: Seamlessly toggle between conventional 360-degree notation and mathematical radians ($2pi$).
All 6 Core Functions: Calculates $sin$, $cos$, $ an$, $csc$, $sec$, and $cot$ simultaneously.
Asymptote & Singularity Protection: Accurately reports Undefined when dividing by zero (e.g. $ an(90^circ)$ or $csc(0^circ)$).
Quick Angle Shortcuts: Instant one-click presets for classic standard angles ($30^circ, 45^circ, 60^circ, 90^circ, 180^circ$).

How to Calculate Trigonometric Functions

Select whether your input is in Degrees or Radians.
Type the angle value into the input box or click one of the preset angle buttons.
Review the sine, cosine, tangent, and reciprocal function values instantly.

Frequently Asked Questions

What is SOH CAH TOA?

SOH CAH TOA is a classic mnemonic memory aid: Sin = Opposite / Hypotenuse, Cos = Adjacent / Hypotenuse, and Tan = Opposite / Adjacent.

Why is tan(90°) undefined?

Because at 90°, the adjacent side length of the triangle becomes 0, and $cos(90^circ) = 0$. Since tangent is $sin/cos$, dividing by zero results in a mathematical singularity (vertical asymptote approaching infinity).

Can angles be negative or greater than 360°?

Yes! Trigonometric functions are periodic waves. An angle of 450° has the exact same trigonometric values as 90° ($450^circ - 360^circ = 90^circ$).

Is this tool free?

Yes, it is 100% free with unlimited calculations.

Trigonometry Functions Calculator

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