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:
than determine the values of a and c and show that b= pi/12
Thank you for your help!
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`