A Ferris wheel has a radius of 50 feet, and its center is 60 feet off the ground. How many points on the Ferris wheel are:

1. 30 feet off the ground?
2. 110 feet off the ground?
3. 5 feet off the ground?

The minute hand on a clock tower is 6 feet long. At 10 minutes after the hour, the tip of the minute hand is 55 feet above the ground. How high above the ground is the center of the clock face? Explain how you know.

A wheel has a radius of 1 foot. The center of the wheel is point \(O\).

A circle divided by 12 congruent central angles. The radius is indicated to be 1 foot. A point on the circle, at the right side of the horizontal diameter, is labeled P.

1. Indicate where point \(P\) will be after the wheel rotates counterclockwise around its center 1 foot. Label this point \(Q\).
2. What is the measure of angle \(POQ\) in radians?
3. Indicate where point \(P\) will be after the wheel rotates counterclockwise around its center \(\frac{3\pi}{2}\) feet. Label this point \(R\).
4. What is the measure of angle \(POR\) in radians?

Angle \(\theta\) corresponds to a point \((x,y)\) on the unit circle in Quadrant I.

1. Which quadrant does \(\theta + \pi\) lie in?
2. In terms of \(x\) and \(y\), what are the coordinates of \(\theta + \pi\)?

Using a unit circle display, give an example of an angle satisfying each inequality.

1. \(A\) so that \(\cos(A) > 0\) and \(\sin(A) < 0\)
2. \(B\) so that \(\cos(B) < 0\) and \(\sin(B) > 0\)
3. \(C\) so that \(\cos(C) < 0\) and \(\sin(C) < 0\)

Suppose angle \(\theta\), in radians, is in Quadrant III of the unit circle. If \(\sin(\theta)=\text-0.45\), what are the values of \(\cos(\theta)\) and \(\tan(\theta)\)?