Unit 3: Geometry and Trigonometry
Topic 3.7: Trigonometric Functions and Graphs Questions
Practice 14 exam-style questions for IB Math AA SL Topic 3.7. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
1State2 marks
2026• Aimnova practice — 3.7.1
On 0° ≤ x ≤ 360°, state the x-values where y = sin x equals 0.
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2026• Aimnova practice — 3.7.1
A wave has a maximum value of 8 and a minimum value of 2. Find its amplitude.
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2026• Aimnova practice — 3.7.1
State two features of the graph of y = tan x that differ from y = sin x.
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2026• Aimnova practice — 3.7.1
For y = cos x on 0° ≤ x ≤ 360°, write down the coordinates of the minimum point.
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2026• Aimnova practice — 3.7.1
State (a) the period and (b) the amplitude of y = sin x.
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2026• Aimnova practice — 3.7.2
State the amplitude and period of y = 4 cos(3x), with x in degrees.
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2026• Aimnova practice — 3.7.2
The graph of y = a cos(bx) has amplitude 6 and period 90°. Find a and b.
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2026• Aimnova practice — 3.7.2
The temperature in a town is modelled by T = 8 sin(15t)° + 18, where t is in hours and the angle is in degrees. Find (a) the maximum temperature and (b) the period of the model.
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2026• Aimnova practice — 3.7.1
A sinusoidal wave reaches a maximum of 12 and a minimum of −4. Find (a) its amplitude and (b) the equation of its midline (principal axis).
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2026• Aimnova practice — 3.7.2
A wheel's height repeats every 30 seconds and is modelled by h = a sin(bt) + d (t in seconds, b in radians). Find the exact value of b.
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2026• Aimnova practice — 3.7.2
A quantity is modelled by y = a sin(bt) + d. Its maximum is 10 and its minimum is 2. Find (a) a and (b) d.
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2026• Aimnova practice — 3.7.1
Explain why y = tan x is undefined at x = 90°.
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2026• Aimnova practice — 3.7.2
Describe the transformations that map y = sin x onto y = sin(x − 45°) + 2.
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2026• Aimnova practice — 3.7.2
A sinusoidal model has amplitude 5, period 8, midline y = 11, and a maximum at t = 2. Write down its maximum and minimum values.
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