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1. Angular measure problem:

A Ferris wheel with a radius of 25.3m makes 2 rotations every minute.

a) Find the average angular speed of the Ferris wheel in radians per second.

b) How far does a rider travel if the ride lasts 5 min?

For a), I did this:

(2π radians/hr) x (2 rotations/min) x (1min/60s)

= (π/15) = 0.21 rad/s

That answer was correct one; however, I'm not sure how it works, because I did the question by looking at an example.

for b),

5 x (π/15) x (1 rotation/2π radians) x (2π(25.3)/1 rotation)

= 126.5π/15

= 26.4 m

This answer is not correct. How do I find the answer?

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The second set of problems deal with tangent curves and their periods. They ask to determine the period and phase shift with respect to y = tan x for each function. The phase shifts I can get right. I know that you can find the period by using (pi/abs(b)), but I the answer in the textbook doesn't match mine, and I don't know why.

a) y = tan (x-(π/4)) ; my answer: π ; book's answer: π/2

b) y = tan (2x-π) ; my answer: (π/2) ; book's answer: π

c) y = tan ((x/2)+(π/2)) ; my answer: (π/3) ; book's answer: π/2

I thought that if something's in a format like tan (2x+1), where there's a number in front of x, then you have to change it to tan 2(x+0.5).

Can anyone explain why my answers are wrong?