A-level · Beta

Trigonometric graphs and radians

Link a rotating unit-circle point to sine, cosine and tangent graphs.

Drag the point around the unit circle, or drag X along the graph.

y=1\sin(1x+0\pi)+0

Tab to a handle, then use the arrow keys. Use the sliders for precise values.

The unit-circle point uses the same angle as the graph’s trigonometric argument.

Input in radians: $x=\frac{1}{4}\pi$
Argument: $\frac{1}{4}\pi$
Period: $\frac{2\pi}{1}$
Output: $\approx 0.7071$

Graph inputs are in radians. Degree sliders also display their equivalent in radians. Discontinuities are left as gaps; numerical values are approximate.

Predict, test and explain

Step 1 of 3

Predict

What is the period of y = sin(2x), with x in radians?

Explore and compare

Choose the investigation above. Predict what will change before you move a control.

Predict

Try it in the simulation. Change one thing at a time.

Explain

Notes and saved values stay in this tab. They disappear when you reload.

Hints, self-check and connections

Try a self-check

Fixed values, separate from the diagram controls.

What is the period of y = sin(2x), with x in radians?

$y=\sin(2x)$

Hint

The sine and cosine period is 2π divided by |b|.

Reveal answer

The input angle completes a full 2π turn when x increases by π.

$\pi$

Build an explanation

Hint 1

The sine and cosine period is 2π divided by |b|.

Hint 2

The tangent period is π divided by |b|.

Hint 3

Convert degrees to radians by multiplying by π/180.

Worked example

This example uses fixed values, separate from the diagram controls.

State the period of y = 3sin(2x) + 1.

The inside multiplier is 2.
Divide the sine period 2π by 2.
The outside multiplier and vertical shift do not affect the period.

Answer: π radians.

Connect this idea

Watch out: Doubling the input multiplier halves the period; it does not double it.

Specification and learning route

AQA E3 · Edexcel Pure 5.3

AS core; A-level extension. This model illustrates selected content; references are not a claim of full coverage or exam-board endorsement.

Useful starting knowledge: Trigonometric ratios; Angles and unit circle; Function transformations.

AQA specification · Edexcel specification