Question 1202354
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Part (i)


The max and min are 10 and -2 respectively.
The midpoint of the max and min is (10+(-2))/2 = (10-2)/2 = 8/2 = 4, which is the value of 'a'. 
This is the midline. 


The function updates to f(x) = 4 - b*cos(x)


Cosine maxes out when x = 0 degrees. 
Cos(x) = cos(0) = 1
When cosine is maxed out, 4 - b*cos(x) will reach its minimum. In this case, the min is -2


4 - b*cos(x) = -2
4 - b*cos(0) = -2
-b*1 = -2-4
-b  = -6
b = 6


Therefore, the function is f(x) = 4 - 6*cos(x)


Answers: <font color=red>a = 4, b = 6</font>


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Part (ii)


f(x) = 4 - 6*cos(x)
0 = 4 - 6*cos(x)
6cos(x) = 4
cos(x) = 4/6
x = arccos(4/6) or x = -arccos(4/6)
x = 48.189685 or x = -48.189685 approximately


The angle -48.189685 is not in the interval 0° ≤ x ≤ 360°, but adding 360 to it will find a coterminal angle.
-48.189685 + 360 = 311.810315


Answers: <font color=red>x = 48.189685, x = 311.810315</font> (both are approximate)


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Part (iii)


I recommend graphing apps such as Desmos and GeoGebra.


Here's the link to the interactive Desmos graph.
<a href="https://www.desmos.com/calculator/roduixexnc">https://www.desmos.com/calculator/roduixexnc</a>
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