## nickersia 2 years ago sinA=-(sprt(3)/2), find two values for cosA without using calculator (x is from 0 do 360 degrees)

1. rachelfreak123

can you use the unit circle?

2. nickersia

Yes I think you can, (something with leters "CAST" - I don't understand it)... And please write detailed explanation, thanks :)

3. rachelfreak123

4. rachelfreak123

uniti cicle is cool because you just find the value for sin and then the value for cos is with it

5. rachelfreak123

i have no idea what CAST is

6. rachelfreak123

did that help?

7. nickersia

Yes it helped for this example, but I still don't know how to the others... For example: If tanA=1/sqrt(3) find 2 values for cosA

8. rachelfreak123

well if it is for other than sin or cos you have to use SOH CAH TOA to find the lenghts of the sides of the triangle all trig crap comes back to triangles....

9. nickersia

Yes, and I use TOA so which leads me to tanX=sinX/cosX In this example sinA=1 and cosA=sqrt(3) which is, I think not possible

10. rachelfreak123

well TOA tells you that the opposite side of the triangle is 1 and the ajacent is root 3, so you just need to find the hypot to figure cos

11. nickersia

|dw:1358706797888:dw|

12. nickersia

If sin is 1 than cos must be 0, that's why I'm confused

13. rachelfreak123

|dw:1358706898345:dw|

14. rachelfreak123

you do not really need the circle part, just a triangle

15. rachelfreak123

the circle would giev you the sign, but atht is uaully just pos and neg

16. phi

If sin is 1 than cos must be 0, that's why I'm confused that is true for the unit circle where the radius is 1 but if you are given tan A = $$\frac{1}{\sqrt{3}}$$ it is easier to say the leg of the opposite side is 1 and the adjacent side is sqrt(3) and figure out the hypotenuse (radius) using pythagoras

17. nickersia

I get the right result +-sprt(3)/2... Thanks, but I'm not sure I understand it clearly yet, I'll try more examples and if I have troubles I'll post :)

18. nickersia

Oh yes, radius doesn't have to be 1, you're right :) Thanks phi

19. phi

I always do these problems using pythagoras to figure out the missing 3rd side. then soh cah toa to get the trig function they want. you can get 2 different values based on whether x is + or - and y is + or -

20. nickersia

|dw:1358707405927:dw| That's how it should look on a circle?

21. phi

btw, cast is just a way to remember which quadrant a trig function is positive See http://mathonweb.com/help_ebook/html/cast.htm but I never need it: I just look at the sign of the x and y values

22. phi

Yes to your picture notice you will get a positive 1/sqrt(3) if you started with -1/-sqrt(3) (that would give you the other angle or CAST (see link) tells you that tan is + is the 3rd quadrant

23. nickersia

Thanks for tips :) Oh, I understand now what it is :D actually you're right, it's not needed, just need to know the coordinates and that sin is on y-axis and cos on x-axis... Thanks a lot, I'm gonna do the rest of the questions :)