Answer: see answers below
Step-by-step explanation:
y = A cos (Bx - C) + D
- A is the amplitude
- Period = 2π/B → B = 2π/Period
- Phase shift = C/B
- D is the vertical shift (aka midline)
Given: A = -3, B = π/20, C = 0, D = 5
1) midline (D) ± amplitude (A) = Max & Min
Max: 5 + 3 = 8
Min: 5 - 3 = 2
2) Midline (D) is given as 5
3) Period = 2π/B = 2π/(π/20) = 40
4) Formula is given as: y = -3 cos (π/20)x + 5
5) change the coordinates of y = cos (x) and as follows:
- x-value: add C and divide by B
- y-value: multiply by A and add D
Note that A = -3, B = π/20, C = 0, D = 5
[tex]\begin{array}{c|ccc|cl}\underline{\qquad x\qquad}&\underline{\qquad y\qquad}&&\underline{\quad (x+C)/ B\quad}&\underline{\quad Ay+D\quad}\\0&1&&0&2&minimum\\\pi/2&0&&10&5&midline\\\pi&-1&&20&8&maximum\\3\pi/2&0&&30&5&midline\\2\pi&1&&40&2&minimum\\\end{array}[/tex]
