Pre Calculus 12
posted by Shreya on .
The height h, in metres, above the ground of a car as a ferris wheel rotates can be modelled by the function h(t) = 18cos(πt/80) +19
what is the minimum height of a car?
do i like subtract 19 from 18 ?
what is the maximum height of a car?
do i add the 19 to 18?
how long does it take for the wheel to revolve once?
80s?
The question below is a different question..
The period in degrees of the graph y = cos4x is?
Is it 45 degrees? I don't get how to solve this?

Just look at the trig part of the function, namely the
cos(....)
the min value of that is 1 and the maximum is +1
so 18cos(..) has a min of 18 and a max of +19
so 18 + 19 = 1 metre, > minimum height of car
and +18 + 19 = 37 > maximum height of car
for y = a cos kx
the period is 2π/k or 360°/k
your value of k is π/80 , you had πt/80 which is (π/80)t
so the period is 2π /(π/80)
= 2π(80/π) = 160
So the period is 160 seconds , if t is defined in seconds
for the 2nd question:
y = cos 4x > compare with y = cos kx
period = 2π/4 radians or 360°/4
= π/2 radians or 90°
Memorize: period = 2π/k or 360°/k