Question

Graph 2: Please help me sketch this graph.

Answer 1

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 = 5/2, B = π/6, C = 0, D = 13/2

1) midline (D) ± amplitude (A) = Max & Min

  Max: 13/2 + 5/2 = 18/2 = 9

  Min: 13/2 - 5/2 = 8/2 = 4

2) Midline (D) is given as 13/2 = 6.5

3) Period = 2π/B  = 2π/(π/6) = 12

4) Formula is given as: y = 5/2 cos (π/6)x + 13/2

5) change the coordinates of y = cos (x) and  as follows:

• x-value: add C then divide by B  
• y-value: multiply by A then add D

Note that A = 5/2, B = π/6, C = 0, D = 13/2

$\begin{array}{c|ccc|cl}\underline{\qquad x\qquad}&\underline{\qquad y\qquad}&&\underline{\quad (x+C)/ B\quad}&\underline{\quad Ay+D\quad}\\0&1&&0&9&maximum\\\pi/2&0&&3&6.5&midline\\\pi&-1&&6&4&minimum\\3\pi/2&0&&9&6.5&midline\\2\pi&1&&12&9&maximum\\\end{array}$