Answer: the points that show the maximum and you have to draw are:
(0, 1.5); (2, 1.5); (4, 1.5);(6,1.5),...
Step-by-step explanation:
1) formula given:
h(t) = 0.5 sin (πt + π/2) + 1
2) You want the points (t, h) where h is maximum.
3) The mamimum of 0.5 sin (πt + π/2) + 1 is when 0.5 sin (πt + π/2) is maximum, and the maximum of 0.5 sin (πt + π/2) is when sin (πt + π/2) is maximum.
4) Now, the maximum of the sine function is 1, so you must solve this equation:
sin (πt + π/2) = 1.
5) As you know, sine function is equal to 1 when the argument is π/2 + 2nπ
So, find the first positive value of t doing
πt + π/2 = π/2
⇒ πt = 0 ⇒ t = 0
So, the first solution is t = 0.
Since the periodicity is 2π, the same value is obtained for t = 0, 2, 4, 6, ... 2n
6) The corresponding height is the same for all those t:
h(0) = 0.5 sin ( 0×t + π/2) + 1 = 0.5×1 + 1 = 1.5.
7) Therefore the points that you have to draw are: (0, 1.5); (2, 1.5); (4, 1.5);(6,1.5)...
I attach a figure just in case you need more help to visualize the answer.