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Please help me solve the following equation and sorry that i cannot provide the...

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samantha96 | Student, Grade 11 | (Level 1) Honors

Posted September 30, 2011 at 10:03 PM via web

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Please help me solve the following equation and sorry that i cannot provide the graph.

The graph is cos, the max is 8 and the min is -92. One cycle begins at 0 and ends at 24. If the relationship of the graph of y and x can be described by the rule:

y=acos(bx)+c

than determine the values of a and c  and show that b= pi/12

Thank you for your help!

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beckden | High School Teacher | (Level 1) Educator

Posted October 3, 2011 at 11:17 AM (Answer #1)

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The period is 24.   Period `= (2pi)/b`

`24 = (2pi)/b`

`b = (2pi)/24 = pi/12`

The amplitude `= (max-min)/2 = (8-(-92))/2=(8+92)/2=50`

so a = 50

so our equation is `y = 50 cos(pi/12x)+c`

Since our maximum is 8 and cos(x)=1 when x=0 we get

8 = 50(1) + c

c = -42

So our function is

y=50 cos(pi/12x) - 42   You can verify this function has a period of 24 and maximum 8 and minimum -92.

Here is a graphof

` y=50 cos(pi/12x) - 42`

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