Unit 3: Geometry and Trigonometry
Topic 3.7: Trigonometric Functions and Graphs Questions
Practice 20 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.
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A wave has a maximum value of 11 and a minimum value of 3. Find its amplitude.
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For y = cos x on 0° ≤ x ≤ 360°, write down the coordinates of the minimum point.
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On 0° ≤ x ≤ 360°, state every value of x for which sin x = 0.
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State (a) the period and (b) the amplitude of y = sin x.
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The depth of water in a harbour is , with in hours. The period of the tide is hours. Show that .
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Show that the graph of is the graph of translated to the right.
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State (a) the period and (b) the amplitude of .
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State the amplitude and period of y = 4 cos(3x), with x in degrees.
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For on , write down the coordinates of the minimum point.
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State two features of the graph of that differ from .
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On 0° ≤ x ≤ 360°, state the x-values where y = sin x equals 0.
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The model , with , has maximum value . Write down the value of .
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The function f(x) = 2 + sin bx, b > 0, has period 6π.
Show that b = 1/3.
Show that b = 1/3.
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On , state the x-values where equals 0.
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The graph of y = 4 cos bx, b > 0, has a maximum point at (0, 4) and the next maximum point is at (π, 4).
Show that b = 2.
Show that b = 2.
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State the amplitude and period of , with x in degrees.
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The function g(x) = −4 cos(πx/10) + 1 can also be written as g(x) = p sin((π/10)(x − q)) + 1, where p > 0. The smallest positive value of q is 5.
For this value of q, write down the value of p.
For this value of q, write down the value of p.
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A wave has a maximum value of 8 and a minimum value of 2. Find its amplitude.
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2021
The height of a seat on a Ferris wheel is metres, minutes after it starts. Find the period of the motion and the greatest height of the seat.
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