Question

help me solve this problem? (attachment)

Answer 1

remember that: sin(x - pi/2) = cos(x) which already simplifies things

Answer 2

They'll be 55 feet above the ground when sin((pi/18)t - pi/2) (Which is just cos((pi/18)t) is 0.
This will happen when (pi/18)t is at (1/2)pi or (3/2)pi

Answer 3

i just dont get how to get both times..

ANSWER CHOICES:
10 seconds and 17 seconds
9 seconds and 27 seconds
9 seconds and 22 seconds
10 seconds and 22 seconds
9 seconds and 17 seconds

Answer 4

plugging 55 as h(t) gives:

\[55 = 55 + 51\cos(\frac{ \pi * t }{ 18 })\]
\[0 = 51\cos(\frac{ \pi*t }{ 18 })\]

cos(x) = 0 when x = pi/2 ± kpi , where k is any integer. so there are actually an infinite amount of answers. this is because cos(x) is a periodic function.

the questions asks within the first 36 seconds.

so it;'s:

\[\frac{ \pi * t }{ 18 } = \frac{ \pi }{ 2 } \pm k \pi\]

take the answers for as many k's that give t between 0 and 36. all of those are answers.