Precalculus B :: Worksheet 3

1. Fill out the unit circle without the use of a calculator. Give exact values.
   • Blank Unit Circle PDF
   • Unit Circle PDF
2. Determine which quadrant the following angles are in:
   1. \(\displaystyle \frac{11\pi}{24}\)
   2. \(\displaystyle \frac{71\pi}{12}\)
   3. \(-1550^\circ\)
3. Make a table of values, and sketch a graph of \(\cot \theta\). Your table should have at least five \(\theta\) values and include one full period.
4. Evaluate the following without the use of a calculator, giving exact answers:
   1. \(\tan(5\pi/6)\)
   2. \(\sec(2\pi/3)\)
   3. \(\cot(-\pi/2)\)
   4. \(\tan(11\pi/6)\)
5. Make the following conversions, rounding to three decimals:
   1. \(37.4^\circ\) to radians
   2. \(1\) radian to degrees
   3. \(11\pi/6\) radians to degrees
6. A 14-inch pizza (14-in in diameter) is cut into eight slices of equal size, what is the area of one slice?
7. Verify the identity \(\displaystyle (\tan^2 \theta) \left(\frac{1}{1-\cos \theta} + \frac{1}{1+\cos \theta}\right) = \frac{2}{\cos^2 \theta}\).
8. Find the four smallest positive numbers \(\theta\) so that \(\tan \theta = 1\).
9. Suppose that \(\pi/2 < \theta < \pi\) and \(\sin \theta = 3/4\). Evaluate:
   1. \(\cos \theta\)
   2. \(\tan \theta\)

10 For the triangle below, \(a=2\) and \(\sin u = 1/3\). Find:

1. \(c\)
2. \(b\)
3. \(\cos u\)
4. \(\tan u\)
5. \(\cos v\)
6. \(\sin v\)
7. \(\tan v\)