Sin/cos questions..HELP PLS!
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Sin/cos questions..HELP PLS!

[From: ] [author: ] [Date: 12-03-16] [Hit: ]
What are the values of a and d?I would reaaaly appreciate it guys!Thanks:)-1.Find the equation of the function with the maximum point at (pi/6, 2) and the next minimum point at (13pi/6, -4).......
1.Find the equation of the function with the maximum point at (pi/6, 2) and the next minimum point at (13pi/6, -4).

2. The function f(x) a sin x+d has a range of -2 less or equal that f(x) less or equal than 18. What are the values of a and d?

I would reaaaly appreciate it guys!
Thanks:)

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1.Find the equation of the function with the maximum point at (pi/6, 2) and the next minimum point at (13pi/6, -4).

Maximum = 2 and minimum = -4 puts middle at average (2+-4)/2 = -1

The distance between the max and minimum is half a period = 13π/6 minus π/6 = 12π/6 = 2π
Consequently the period of our function is 4π

Amplitude is 2 -(-1) = 3



With amplitude of 3 and period of 2π
and max at zero, minimum at π

our function would be

y = 3 cos x

To get the period to 4π

It becomes

y = 3 cos[ x/2]

that leaves maximum at zero and minimum at 2π
To get the max point over to π/6 and shift minimum to 13π/6

it becomes

y = 3 cos[½(x-(π/6))]

This has max at 3 and min at -3
To move max down to do and min down to -4 we have to subtract 1

so the function is

y = 3 cos[½(x-(π/6))] -1


2. The function f(x) a sin x+d has a range of -2 less or equal that f(x) less or equal than 18. What are the values of a and d?


Range is -2≤f(x)≤18

size of range is 18 -(-2) = 20

amplitude is half of that 20 which is 10 so a=10

Now d is the upward or downward shift, upward if positive and downward if negative.

The average of -2 and 18 is [18 +(-2) ]/2 = 16/2 = 8

That is an upward shift of 8 units so d=8
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