## anonymous 5 years ago Find the exact value of the following expression (multiple choice)

1. anonymous
2. anonymous

3. anonymous

method. i'll figure out the answer from the method..that way, i learn the method and figure the answer

4. anonymous

or calculator?

5. anonymous

k

6. anonymous

number 1. think of a number (angle) between 0 and pi whose cosine is $\frac{\sqrt{3}}{2}$

7. anonymous

look at trig cheat sheet here http://tutorial.math.lamar.edu/cheat_table.aspx if you do not remember

8. mathteacher1729

Drawing pictures is SUPER helpful. The trig sheet Satellite mentioned is also very nice. :)

9. anonymous

oh i only nueed help on number 17. thanks though

10. anonymous

aaahhhhhhhh

11. mathteacher1729

Still,l a pic would help. Lemmie sketch out one... brb.

12. anonymous

addition angle formula: $sin(a+b)=sin(a)cos(b)+cos(a)sin(b)$

13. mathteacher1729

You won't even have to do that, I think, cuz you have to do the inverse sin & cos stuff inside the main sin argument.

14. anonymous

thats what i thought..at math teacher

15. anonymous

i just dont know how to go about solving it

16. anonymous

typeset is goofy but i assume it means $sin(sin^{-1}(\frac{2}{3}) + cos^{-1}(\frac{1}{3}))$

17. anonymous

yuppers. thats what it means

18. anonymous

put $a=sin^{-1}(\frac{2}{3}), b=cos^{-1}(\frac{1}{3})$

19. anonymous

use formula above. you aready know $sin(sin^{-1}(\frac{2}{3}))=\frac{2}{3}$

20. anonymous

you need $cos^{-1}(\frac{2}{3})=\frac{\sqrt{5}}{3}$ by pythagoras

21. anonymous

oops typo

22. anonymous

you need $cos(sin^{-1}(\frac{2}{3}))=\frac{\sqrt{5}}{3}$

23. anonymous

by pythagoras.

24. mathteacher1729

Here is the first part.

25. anonymous

ahh the pythagorean thm

26. anonymous

what math teacher said. you only need to find $sin(cos^{-1}(\frac{1}{3}))=\frac{\sqrt{2}}{3}$

27. anonymous

now you have everything you need to plug in to the "addition angle" formula

28. anonymous

but i think you must use the formula now. you have all 4 numbers that you need. $sin(a)=\frac{2}{3}$ $cos(a)=\frac{\sqrt{5}}{3}$

29. anonymous

$sin(b)=\frac{\sqrt{2}}{3}$ $cos(b)=\frac{1}{3}$

30. anonymous

write out the formula, substitute the numbers, and be done.

31. anonymous

right. gimme a sec.

32. anonymous

whoooooooooooops

33. anonymous

$sin(b)=\frac{\sqrt{8}}{3}$

34. anonymous

fraid both math teacher and i made a mistake.

35. anonymous

its okay. i'm still working on it. thanks

36. anonymous

if you look at the picture math teachers sent unfortunately the second triangle is wrong. adjacent side is 1, hypotenuse is 3, opposite side should be ${\sqrt{8}}=2\sqrt{2}$

37. anonymous

get $\frac{2}{3}\times \frac{\sqrt{5}}{3}+\frac{1}{3}\times \frac{2\sqrt{2}}{3}$

38. anonymous

is the answer for number 17 "A"? thats what i'm getting. http://tigger.uic.edu/~calkafka/spring2011math121practiceexam3.pdf

39. mathteacher1729

Oh my gosh, I can't believe I did that. :( here is the corrected version.

40. anonymous

dont worry mathteacher. satellite clarified. i'm debating on whether its A or B for number 17 in the link i posted

41. anonymous

A yes!

42. anonymous

SWEET! thanky you so much!

43. anonymous

welcome