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Sin-Cos Converter | Convert between sine & cosine

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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

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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.
Why can't sine be found from cosine alone?
Because sin²θ + cos²θ = 1 gives sin θ = ±√(1 − cos²θ) — two answers, one positive and one negative. The sign depends on the quadrant: sine is positive in quadrants I and II, negative in III and IV. The angle (or at least its quadrant) is needed to pick the correct sign.
How do degrees convert to radians and back?
Multiply degrees by π/180 for radians, or radians by 180/π for degrees — 90° equals π/2, about 1.5708 rad. The conversion shows both units alongside the ratio, which prevents the classic mistake of feeding degrees into a formula that expects radians.
Which exact values are worth memorizing?
The special angles 0°, 30°, 45°, 60°, 90°: sin 30° = 1/2, sin 45° = √2/2, sin 60° = √3/2, with cosines mirrored (cos 30° = √3/2, and so on). The converter displays these exact forms instead of rounded decimals for the common angles. Recognizing them makes identities and integrals much faster.
Where does tangent fit in?
Tangent links the two ratios: tan θ = sin θ ÷ cos θ. It is undefined at 90° and 270°, where cosine is zero — the vertical asymptotes on the tangent graph. Including tan means you can move between all three ratios for the same angle.

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