Science:Math Exam Resources/Courses/MATH102/December 2013/Question A 07
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Question A 07 

The number of sunspots (solar storms on the sun) varies with a period of roughly 11 years reaching a high of 120 and a low of 0 sunspots detected. A peak of 120 sunspots was detected in the year 2000. Which of the following trigonometric functions could be used to approximate this cycle? (a) (b) (c) (d) (e) 
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

One way of solving this problem is to simply plug into the given possibilities and check if you get the number of sunspots that were detected in the year 2000. 
Hint 2 

A more methodical method of approaching the problem is as follows:
or for some function .

Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 1 

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Please rate my easiness! It's quick and helps everyone guide their studies. Substituting into the given possibilities gives
Therefore, the answer is . 
Solution 2 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. A more methodical method of approaching the problem is as follows:
or for some function .
for some other function .
since the peak of the cosine function is at 0 (up to integer multiples of ). If we used the sine function, we would have and since the peak of the sine function occurs at up to integer multiples of .
or The latter is a possible choice in the question, and so the answer is . 