June 2009 Exam, Part 2, Qu. #13

13. The value of csc(5 pi/3):
a. -2
b. -2/√3
c. 2
d. 2/√3

Solution:
1. Look on unit circle and find 5pi/3
2. It's in quadrant 4 at 300 degrees

3. csc= 1/y

4. At that place on the unit circle y= -√3/2
5. Since csc= 1/y divide 1 by -√3/2 (multiply numerators then denminators)
6. You should get 2/-√3 Which is the answer to the question according to the site (Answer: b)
7. If you choose to go a step further and rationalize the denominator, multiply both the numerator and demonenator by -√3
8. This will give you -2√3/3