Watch out
Giving 360° as the tangent period.
Scottish National 5 Mathematics
National 5 Maths Trigonometric graphs
Recognise and interpret basic and transformed sine, cosine and tangent graphs.
Formula reference
Check the National 5 rules and formulae linked to this topic.
Which method?
Match exam clues to a suitable method.
Before you start
- Know the exact sine and cosine values at key angles.
- Read coordinates from axes accurately.
- Recognise period as the length of one complete cycle.
Explanation
The sine and cosine graphs repeat every 360°. The tangent graph repeats every 180°.
The basic sine graph starts at 0 and rises; the basic cosine graph starts at 1. Both have range −1 to 1.
In y = a sin x or y = a cos x, |a| is the amplitude. Adding d moves the whole graph vertically and changes its range.
Key formulae and rules
- period of sin x and cos x = 360°
- period of tan x = 180°
- amplitude of a sin x or a cos x = |a|
Check
Check the amplitude, period and key coordinates against the expected sine, cosine or tangent shape.
Exam tip
Use intercepts, maximum/minimum values and period together rather than identifying a graph from one point.
Worked examples
Worked example 1
Recognise sine
A trig graph passes through (0°, 0), rises to 1 at 90° and returns to 0 at 180°.
- It starts at zero.
- It reaches a maximum at 90°.
- These are sine-graph features.
Answer: The graph is y = sin x.
Worked example 2
Find a period
Find the period of y = sin(2x).
- The sine period is 360°.
- The multiplier 2 halves the horizontal period.
- 360 ÷ 2 = 180
So: The period is 180°.
Worked example 3
Find a range
Find the range of y = 3 cos x + 2.
- 3 cos x ranges from −3 to 3.
- Adding 2 shifts both limits up 2.
Answer: -1 ≤ y ≤ 5.
Watch out
- Giving 360° as the tangent period.
- Confusing amplitude with period.
- Changing only the maximum when a graph moves vertically.