## anonymous 5 years ago Actually, I stand corrected with my question. it is how does cos(-5pi/3)= -square root of 2/2?

1. amistre64

its proved usually by drawing the angle inside the unit circle

2. anonymous

i saw that unit circle and closed the trig book in fear and ran the other way!!! Do yo have to use the unit circle? If so, how does one read it? Btw, hello again from Illinois. Back for more torture, huh? ; )

3. amistre64

you can use a triangle as well, bu the unit scircle is a better fit; im drawing one u p for you right now

4. amistre64

cos -5pi/3 is just about a full circle so; we can call it pi/3 = 60 cos(60) = 1/2 so i dont see a way to 'prove' it becasue its contradictory it first glance

5. anonymous

yes you have to use the unit circle. put the 'reference triangle' inside it. or just use a cheat sheet. best one is here http://tutorial.math.lamar.edu/cheat_table.aspx

6. anonymous

actually it does not!

7. amistre64

8. amistre64

the cos of that angle = 1/2 regardless of any other measures

9. anonymous

$cos(-\frac{5\pi}{3})+=\frac{1}{2}$

10. anonymous

so looking at this unit circle. i see on there that 225 degrees, for example, is 5pi/4. but what if i wanted cos or sin? like in my original ? which asks cos(-5pi/4). does it not matter about the cos or sin? will the answer in square root always be the same?

11. anonymous

$=$cos(-5pi/3) =cos(5pi/3) =$cos( 2 \pi - 5\pi/3)$ $=\cos(\pi / 3)$ = 1/2

12. amistre64

cos is the x value of the angle dropped down to the x axis

13. amistre64

sin is the y value

14. amistre64

like this

15. amistre64

16. anonymous

hey are you going to be around today? I am goiong to go investigate this unit circle and maybe I can get somewhere with it then! Thanks again, of course! Too bad you live so far away; i would pay a ton of money for your tutoring math abilities!

17. amistre64

a ton eh ;) i should be around till about 5. cant say much for after that tho