The diagram shows part of the graph of the function $y = p \, ext{cos} \, qx + r$ - Scottish Highers Maths - Question 4 - 2015
Question 4
The diagram shows part of the graph of the function $y = p \, ext{cos} \, qx + r$.
Write down the values of $p$, $q$, and $r$.
Worked Solution & Example Answer:The diagram shows part of the graph of the function $y = p \, ext{cos} \, qx + r$ - Scottish Highers Maths - Question 4 - 2015
Step 1
Write down the values of $p$
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Answer
From the graph, the maximum value is 4 and the minimum value is -2. The amplitude A can be calculated as:
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Answer
The period T of the cosine function can be observed as the distance between two consecutive peaks. From the graph, the distance from 0 to rac{ ext{π}}{2} corresponds to one quarter of the period. Therefore, the full period is:
T = 2 imes rac{ ext{π}}{2} = ext{π}
The relationship between the period and q is given by:
T = rac{2 ext{π}}{q}
Equating this with the observed period:
ext{π} = rac{2 ext{π}}{q}
Solving for q gives:
q=2
Step 3
Write down the values of $r$
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Answer
The midline of the graph can be found as the average of the maximum and minimum values:
