Ch 5.1-5.3

The Unit Circle

100

Find all numbers t such that \[({2\over 7},t)\] is a point on the unit circle

What is \[\pm{3\sqrt{5}\over 7}\]?

200

What angle (in degrees) corresponds to a circular arc on the unit circle with length \[{\pi\over 5}\]?

What is 36 degrees?

300

Suppose an ant walks counterclockwise on the unit circle from the point (1,0) to the endpoint of the radius that forms an angle of 80 degrees with the positive horizontal axis. How far has the ant walked?

What is \[{4\pi\over 9}\]?

400

Find the lengths of both circular arcs on the unit circle connecting the point \[({1\over 2},{\sqrt3\over 2})\] and the point that makes an angle of 160 degrees with the positive horizontal axis.

What is \[{5\pi\over 9} and {13\pi\over 9}\]

Radians

100

Convert 110 degrees to radians.

What is \[{11\pi\over 18}\]

200

Convert \[{\pi\over 16}\] to degrees.

What is 11.25 degrees?

300

Find the lengths of both circular arcs of the unit circle connecting the points (1,0) and the endpoint of the radius that makes an angle of 4 radians with the positive horizontal axis. (leave pi in your answer)

What is 4 radians, and 2pi - 4?

400

For a 12 inch pizza, find the area of a slice with angle \[{2\over 9}\] radians.

What is 4 square inches?

500

Suppose a slice of a 10 inch pizza has an area of 25 square inches. What is the angle of this slice?

What is 2 radians?

Cosine and Sine

100

Find the smallest number \[\theta\thinspace larger \thinspace than \thinspace 3\pi\] such that \[cos\theta = {-1\over 2}\]

What is \[{10\pi\over 3}\]

200

Find the 4 smallest positive numbers \[\theta\thinspace such\thinspace that\thinspace sin\theta = 0\]

What is \[\pi, 2\pi, 3\pi, 4\pi\]

300

Suppose \[{\pi\over 2}<\theta<\pi\thinspace and\thinspace cos\theta={-2\over 5}.\] \[Evaluate\thinspace sin\theta\]

What is \[\sqrt{21}\over 5\]