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°.
Higher Mathematics
Higher Maths Trigonometric graphs
Practise trigonometric graphs for Scottish Higher Mathematics with worked examples, clear methods and original interactive questions. Interpret amplitude, period, phase shift and related transformations of sine, cosine and tangent.
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
Amplitude is the vertical distance from the midline; period is the horizontal length of one cycle
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 = twice between 0° and 360°.
- Find the reference angle.
- Use the graph or quadrants to locate all intersections.
So: For sin θ = , 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.
Related Higher Maths topics
Continue with the methods that connect most closely to this topic.