MATH102 December 2017
• Q1 • Q2 • Q3 • Q4 • Q5 • Q6 • Q7 (a) • Q7 (b) • Q7 (c) • Q8 • Q9 (a) • Q9 (b) • Q9 (c) • Q10 (a) • Q10 (b) • Q10 (c) • Q10 (d) • Q11 (a) • Q11 (b) • Q12 (a) • Q12 (b) • Q12 (c) • Q12 (d) • Q13 (a) • Q13 (b) • Q13 (c) • Q13 (d) • Q14 (a) • Q14 (b) • Q15 (a) • Q15 (b) • Q16 •
Question 15 (a)
A grasshopper caught in a spiderweb rhythmically kicks its legs, causing the web to bounce up and down. The height of the grasshopper (in cm) after seconds is
(a) What is the period of this function?
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!
The period of the sine function is . In other words, for any , .
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By the Hint, using the periodicity of the sin function, we have
Factoring , we have
This implies that the period of is .
Since a constant multiple of a function (a vertical dilation of a graph) and a translation don't change the period of a function, the period of is same with that of .
More precisely, let us multiply by and add to both sides:
This means that So the period of is .
Answer: the period is .