Question

Use the CALC features of the TI to answer the following. Show what you put into the calculator & what CALC feature you used. Round to the nearest tenths.

The equation h = 20 cos (π/4 (t-3)) + 23 tells how high above the ground a ferris wheel car is at any given time. h is measured in feet; t is measured in seconds.

1) What is the second time that the ferris wheel car is 18 ft above the ground?

2) Give an expression in laymen's terms for the times at which the car is at its highest point.

Answer 1

18 = 23 - 5
so
when is 20 cos (π/4 (t-3)) = -5 ?

cos (pi/4(t-3)) = -1/4 = -.25

use inverse cos in radians mode

pi/4(t-3) = 1.823 radians
and also 2 pi - 1.823 = 2.889 radians
(that is the second time, on the way down)

now I think you can get t from
(pi/4)(t-3) = 1.823 etc

for part 2 it is when
(pi/4) (t-3) = 0 because cos 0 = 1 max
or t = 3 and every period after that
t= 3
pi/4 * (8) = 2 pi
so T = 8
3, 11 , 19 etc