## anonymous 5 years ago Please tell me how to do this problem Evaluate : sin(1/4 pie) A) 1 B) 0 C) sqrt 2 /2 D None of these

1. anonymous

C) sqrt 2 /2

2. anonymous

How did u get this?

3. anonymous

look at the unit circle on the last page of this cheat sheet.

4. anonymous

c

5. anonymous

you will see that at $\frac{\pi}{4}$ both the first and second coordinate on the unit circle is $\frac{\sqrt{2}}{2}$ so both sine and cosine are the same there

6. anonymous

you can also do it directly using a triangle but this one comes up so often it is best to memorize it

7. anonymous

ok then how would i do a problem like tan( -337 pie /4 )

8. anonymous

oh lord. first of all you best find a point between 0 and 2 pi that is coterminal with $\frac{-337\pi}{4}$

9. myininaya

pie?

10. anonymous

myininaya will who you how, because last time i did this i got in a huge discussion mmmm pie

11. myininaya

apple pie?

12. anonymous

o.o

13. myininaya

chicken pot pie

14. anonymous

ok fine. lets to it the easy (for me) way $\frac{-337}{4}=-84\tfrac{1}{4}$ and since 2 divides 84 evenly this angle is co terminal with $-\frac{\pi}{4}$

15. anonymous

rhubarb pie

16. myininaya

what value does pie hold?

17. myininaya

does pie=pi?

18. anonymous

$\sin(-\frac{\pi}{4})=-\frac{\sqrt{2}}{2}, \cos(-\frac{\pi}{4})=\frac{\sqrt{2}}{2}$ and since tangent is the ratio of sine over cosine you get -1

19. anonymous

so the final answer is -1?

20. anonymous

yup

21. anonymous

and if you doubt me, here is proof http://www.wolframalpha.com/input/?i=tan%28-337+pi%2F4%29

22. anonymous

$\color{blue}{\text{sk}}\color{red}{\pi}\color{blue}{\text{y}}$

23. anonymous

that, my myininaya, was for you

24. myininaya

pie?

25. anonymous

c'mon. what did i write?

26. myininaya

pi?

27. anonymous

nope

28. anonymous

what do you see there?

29. myininaya

lol this pie concerns me

30. myininaya