y+-10cos3x+12 , where x is in seconds, and y is the height above the ground in metres. Answer
the following questions.
a. How long does it take to complete one rotation?
b. What is the diameter of the Ferris wheel?
c. Where is the location of the axle of the Ferris wheel?
d. What is the height of a rider 45 seconds into the ride?
y +/- 10cos(3x) + 12 is not an equation.
i believe your equation is:
y = +/- 10cos(3x) + 12
this is actually 2 equations.
first equation is y = + 10cos(3x) + 12
second equation is y = - 10cos(3x) + 12
you can graph both equations at the same time and this is what you will get:
what this equation tells you is that the high point of the ferris wheel is 22 feet above the ground and the low point of the ferris wheel is 2 feet above the ground.
this puts the center of the ferris wheel at 12 feet above the ground with a diameter of 20 feet.
if you look at the high points of either equation, you will see that going from one high point to the other high point takes 120 seconds.
that's how long it takes for the ferris wheel to complete one full revolution.
45 seconds into the ride, one of the equations will tell you that the rider is 4.93 feet above the ground and the other equation will tell you that the rider is at 19.07 feet above the ground.
these riders are on opposite sides of the ferris wheel so that makes sense.
you could have modeled the rotation of the ferris wheel with only one of the equation.
if i had to choose which one, i would have chosen y = - 10*cos(3x) + 12 because that equation causes the rider on the ferris wheel to be at the bottom of the circle traveled by the ferris wheel when x = 0.
here is the graph of that equation alone.
you can see that it goes from bottom to bottom in 120 seconds and that the rider is 19.07 feet above the ground in 45 seconds and that the diameter is the difference between the high point of 22 feet above the ground and the low point of 2 feet above the ground and that the center is at 12 feet above the ground which makes the radius of the ferris wheel equal to 10 feet.
here is a picture of the ferris wheel with numbers applicable to the equation of y = -10 * cos(3x)+ 12 only.
since the ferris wheel goes around 360 degrees in 120 seconds, it is traveling at the rate of 3 degrees per second.
in 45 seconds, that puts it as the 135 degree mark, assuming that the 0 degree mark is at the bottom of the circle that the ferris wheel travels.