anonymous one year ago Find the exact value of cos-1the quantity square root of three divided by two.

1. anonymous

$\cos^{-1} (\sqrt{3}/2)$

2. Nnesha

we take inverse of ratio to find an angle so you need an angle when cos theta = sqrt{3}/2 1st) you can use unit circle 2nd) calculator 3rd) familiar with 30-6-90 /45-45-90 triangle theorem

3. Nnesha

btw in the order pair (x,y) cos = x sin = y

4. anonymous

so what do i do next

5. Nnesha

1st) you can use unit circle 2nd) calculator 3rd) familiar with 30-6-90 /45-45-90 triangle theorem 3 ways to find an answer pick one :=)

6. Nnesha

it's 30-60-90 ****

7. anonymous

unit circle i guess

8. Nnesha

alright |dw:1444053304744:dw| at what angle cos = sqrt{3}/2

9. anonymous

30 and 60

10. anonymous

no just 30

11. Nnesha

there should be two angle when cos =sqrt{3}/2 remember it's reflected over they axis |dw:1444053390030:dw|

12. Nnesha

the*

13. anonymous

i thought you only needed one but okay then 330

14. Nnesha

well there are two you should write both as an ansaawer just in case if they are looking for more than one value hmm

15. anonymous

okay so whats the next step?

16. Nnesha

that's it

17. Nnesha

18. anonymous

but its the arc cosine

19. anonymous

20. Nnesha

right when we need an angle we take invs of ratio so that's why it's arccos

21. Nnesha

ohh okay formula to convert degree to radian $\huge\rm rad=\frac{ \pi}{ 180} \times degree$

22. anonymous

well which angle do i use

23. Nnesha

both angles 30 and 330

24. anonymous

cant i just use the radian it has on the unit circle next to it

25. Nnesha

yes you can

26. Nnesha

you will get the same answer

27. anonymous

but both are an answer choice

28. anonymous

which one is right

29. Nnesha

ohh so you can pick only one ?

30. anonymous

yes

31. Nnesha

i'll pick 30 bec that's the angle where it starts

32. Nnesha

330 is areflection

33. anonymous

so pi/6?

34. Nnesha

looks good

35. anonymous

thank you

36. Nnesha

yw