Exercises for Question Type 16: Working with sinusoidal models to calculate values of parameters

Question 1

Skill question

Find the value of $k$ such that the function $y = 5 sin (k x)$ has a frequency of 4.

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Question 2

Skill question

Compute the value of $y$ when $x = \frac{π}{8}$ for $y = 8 cos (4 x) + 2$ .

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Question 3

Skill question

Find the amplitude and period of $y = 5 sin (2 x) + 3$ .

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Question 4

Skill question

Determine the period of $y = 9 cos (5 x) + 11$ .

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Question 5

Skill question

Given $y = A cos (2 x - \frac{π}{2}) + 5$ , identify the vertical shift and phase shift.

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Question 6

Skill question

Determine the value of $k$ such that $y = 3 cos (k x - \frac{π}{3}) + 2$ has period 6.

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Question 7

Skill question

For $y = 4 cos (3 x + \frac{π}{6}) - 1$ , find the period and phase shift.

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Question 8

Skill question

Write a sinusoidal model of the form $y = 3 sin (k x) - 2$ with amplitude 3, period $4 π$ , no phase shift, and vertical shift $- 2$ . Find $k$ .

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Question 9

Skill question

For $y = 6 sin (\frac{x}{2} + \frac{π}{4})$ , find the period and angular frequency.

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Question 10

Skill question

Find the frequency of $y = 7 sin (4 x) - 6$ .

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Question 11

Skill question

Find the period of $y = 2 sin (\frac{π x}{3}) + 1$ .

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Question 12

Skill question

Determine the $x$ -coordinate of the first positive peak of $y = 3 cos (2 x) + 4$ .

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IB Mathematics Applications & Interpretation Question Type 16: Working with Sinusoidal Models to Calculate Values of Parameters Exercises