Question

1. the top and bottom were torn off the graph. a maximum occurred at 3 and the next minimum at 7.5 seconds. christina knew that the height of 4 was first arrived at 0.9095 seconds. use symmetry to calculate when the next two times the height is 4.

Explanation:

Step1: Find half-period

The distance between max and min is half the period.
$\frac{T}{2} = 7.5 - 3 = 4.5$

Step2: Find full period

Double the half-period to get full period.
$T = 2 \times 4.5 = 9$

Step3: Symmetry around max (first time)

The first height=4 is symmetric to the second time around the maximum at $t=3$. Let the second time be $t_2$.
$3 - 0.9095 = t_2 - 3$
$t_2 = 3 + (3 - 0.9095) = 5.0905$

Step4: Add period for third time

The third time is the first time plus the full period.
$t_3 = 0.9095 + 9 = 9.9095$

Answer:

The next two times the height is 4 are 5.0905 seconds and 9.9095 seconds.