CalcaTools

Sin-Cos Converter | Convert between sine & cosine

Convert between sine and cosine, and degrees and radians, using the unit-circle identities with the working shown. Includes the exact values for common angles — ideal for trigonometry homework and physics.

Last updated: June 2026 · Free · No sign-up required

Results

Enter values above and click Calculate to see your result instantly.

Inside the Sin Cos Converter

Behind the inputs above sits one rule: sin²θ + cos²θ = 1; tanθ = sinθ ÷ cosθ; rad = deg × π/180. The tool evaluates it instantly with the values you enter.

Scroll past the converter for a quick-reference table, a step-by-step methodology with a fully worked example, and answers to the questions people most often ask about sin cos calculator.

Quick reference

Anglesincostan
0°010
30°0.50.86600.5774
45°0.70710.70711
60°0.86600.51.7321
90°10undefined

info Sin Cos Converter

Free math calculator — enter your numbers and get an instant, accurate result.

info Private by design

Everything runs locally in your browser. No uploads, no accounts, no tracking.

info Works everywhere

Fully responsive and mobile-friendly — calculate on any device, any time.

info Educational

Includes the formula and step-by-step explanation so you understand the math, not just the answer.

Interpretation guide

QuadrantSigns (sin / cos / tan)
0–90°+ / + / +
90–180°+ / − / −
180–270°− / − / +
270–360°− / + / −

lightbulb Worked example

Let's say you are using the Sin Cos Converter. Converts sin cos using sin²θ + cos²θ = 1, right in your browser. Enter the values that match your situation into the input fields and press calculate — using realistic numbers makes the result directly useful for you.

Result: The calculator instantly applies the formula sin²θ + cos²θ = 1; tanθ = sinθ ÷ cosθ; rad = deg × π/180 and returns the result with appropriate precision.

What this means: Read the result in the context of what you are measuring. The step-by-step breakdown lets you confirm the math and understand which input most affects the outcome.

Formula & methodology

Formula: sin²θ + cos²θ = 1; tanθ = sinθ ÷ cosθ; rad = deg × π/180

How sine and cosine convert

The tool applies the unit-circle identities sin²θ + cos²θ = 1 and tanθ = sinθ ÷ cosθ, and converts angles with rad = deg × π ÷ 180. On the unit circle, cos(θ) is the x-coordinate and sin(θ) the y-coordinate of the point at angle θ, which is why one determines the other.

Example: if sin(30°) = 0.5, then cos(30°) = √(1 − 0.25) ≈ 0.866, and tan(30°) = 0.5 ÷ 0.866 ≈ 0.577.

Reading the result: the two functions are phase-shifted by 90° — sin(θ) = cos(90° − θ) — so converting between them is a matter of shifting the angle. The exact values at the standard angles (30°, 45°, 60°) come from the special right triangles and are shown alongside the decimals.

Authoritative source: Wolfram MathWorld

Frequently asked questions

What are sin and cos of 30 degrees?
The Sin Cos Converter is free, private, and accurate: it runs entirely in your browser (no uploads, no accounts), applies the standard calculation, and explains each step so you can verify the result. Converts sin cos using sin²θ + cos²θ = 1, right in your browser. There is no limit on usage, and it works on any device.
How are sine and cosine related?
They are the two coordinates of a point on the unit circle: cos(θ) is the x-coordinate and sin(θ) the y-coordinate at angle θ. This gives the fundamental identity sin²θ + cos²θ = 1, and the phase relationship sin(θ) = cos(90° − θ). One is the other shifted by 90°, which is why they are paired in the converter.
Why is tan 90° undefined?
Because tan(θ) = sin(θ) ÷ cos(θ), and cos(90°) = 0 — dividing by zero has no value. As the angle approaches 90°, the tangent grows without bound, which is why the graph has a vertical asymptote there. In the unit circle, the tangent line is vertical at 90°, so it never intersects the x-axis. The converter flags this rather than returning infinity.
How do I convert degrees to radians?
Enter the required values into the input fields and press the calculate button. The tool applies the formula sin²θ + cos²θ = 1; tanθ = sinθ ÷ cosθ; rad = deg × π/180 and returns the result with a short explanation of each step, so you can check the working yourself.
Which common angles have exact values?
The standard angles give exact surds: sin 30° = 1/2, sin 45° = √2/2 ≈ 0.7071, sin 60° = √3/2 ≈ 0.8660, and cos values mirror them — cos 30° = √3/2, cos 45° = √2/2, cos 60° = 1/2. These come from the 30-60-90 and 45-45-90 triangles. The converter shows the exact forms alongside the decimals for these angles.
What does the Sin Cos Converter do?
Converts sin cos using sin²θ + cos²θ = 1, right in your browser. The calculator takes your inputs, applies the standard calculation, and returns a clear result so you can make an informed decision without doing the math by hand.
What formula does the Sin Cos Converter use?
It relies on the identities sin²θ + cos²θ = 1 and tanθ = sinθ ÷ cosθ, converting between the two ratios for the same angle. It also converts degrees to radians with rad = deg × π/180. Given the sine of an angle you can find the cosine, and vice versa, which is handy for right-triangle problems where only one ratio is known.
Is the Sin Cos Converter free and private?
Yes — the Sin Cos Converter. There is no sign-up, no paywall, no trial, and no limit on how many calculations you can run. CalcaTools covers its costs with non-intrusive display advertising, so the calculator itself never asks for payment or restricts any feature.
How accurate is the Sin Cos Converter?
The Sin Cos Converter applies the standard formula: sin²θ + cos²θ = 1; tanθ = sinθ ÷ cosθ; rad = deg × π/180. It is tested against published worked examples before launch and uses native double-precision arithmetic, so results are accurate to typical precision for the values you enter — with no intermediate rounding that could distort the answer.

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