Worked example 1
Read amplitude and period
State the amplitude and period of y = 3sin(2θ).
- The coefficient outside sin is 3.
- The coefficient of θ is 2.
- Calculate 360°/2
Answer: Amplitude 3, period 180°.
Back to Higher Mathematics
Higher Mathematics
Trigonometric graphs
Interpret amplitude, period, phase shift and key features of trig graphs.
Before you start
- Know the basic shapes of sin θ, cos θ and tan θ.
- Read axes and intervals carefully.
- Connect graph transformations to amplitude and period.
Explanation
Trig graphs show repeating behaviour. Sine and cosine have amplitude and period; tangent repeats with vertical asymptotes. Transformations change the height, spacing and position of the graph.
Solving from a trig graph means reading all intersections in the given interval.
Visual support
Method and rules
- For y = a sin θ or y = a cos θ, amplitude = |a|.
- For y = sin(bθ) or y = cos(bθ), period = 360°/b.
- Vertical shifts change the midline.
- Phase shifts move the graph horizontally.
Worked examples
Worked example 2
Use intersections
A sine graph crosses y = 12 twice between 0° and 360°.
- Find the reference angle.
- Use the graph or quadrants to locate all intersections.
So: For sin θ = 12, θ = 30°, 150°.
Watch out
- Calling period the same as amplitude.
- Finding only one graph intersection.
- Ignoring a vertical shift when reading the midline.
- Mixing degrees and radians.
Exam reminder
Quote angles in the units used by the question. If the interval is 0° ≤ θ < 360°, do not include 360° unless allowed.