Precalculus B :: Worksheet 1

Convert \(18^\circ\) to radians.
Convert \(\displaystyle \frac{17\pi}{12}\) to degrees.
How many degrees are in one radian?
Convert 3 radians into degrees.
Which quadrant is \(1025^\circ\) in?
Which quadrant is \(\displaystyle \frac{33\pi}{6}\) in?
Find \(\sin \theta\) if \(\cos \theta = -12/13\) and \(\theta\) is in quadrant II.
Find the values of \(\cos \theta\) and \(\sin \theta\) for following values of \(\theta\):
1. \(\theta = \pi/2\)
2. \(\theta = 3\pi/2\)
3. \(\theta = \pi/4\)
4. \(\theta = 7\pi/6\)
5. \(\theta = 11\pi/6\)
6. \(\theta = 5\pi/4\)
7. \(\theta = 3\pi/2\)
8. \(\theta = 36\pi\)
9. \(\theta = 37\pi/4\)
10. \(\theta = -5\pi/12\)
Given the radius \(r\) of a circle and a central angle \(\theta\) in radians, derive formulas for the length of an arc with central angle \(\theta\) and the area of a sector with central angle \(\theta\).
For an angle \(\theta = \pi/4\) and a radius \(r = 12\):
1. What is the length of an arc intercepted by a central angle of \(\theta\) on a circle of radius \(r\)?
2. What is the area of the sector with central angle \(\theta\) in a circle of radius \(r\)?