kittiwitti1
  • kittiwitti1
http://prntscr.com/9av46p Do I not divide the 2 in the cos function out to get the answer?? o-0
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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jim_thompson5910
  • jim_thompson5910
how did you get those two answers?
jim_thompson5910
  • jim_thompson5910
hopefully you agree that if \[\Large \cos(2x) = \frac{\sqrt{3}}{2}\] then \[\Large 2x = \frac{\pi}{6} + 2\pi*n \ \ \text{ or } \ \ 2x = -\frac{\pi}{6} + 2\pi*n\]
kittiwitti1
  • kittiwitti1
I don't exactly remember but I think it involved dividing the 2 out of the cos2(x)

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jim_thompson5910
  • jim_thompson5910
do you see how I got \[\Large 2x = \frac{\pi}{6} + 2\pi*n \ \ \text{ or } \ \ 2x = -\frac{\pi}{6} + 2\pi*n\]
kittiwitti1
  • kittiwitti1
Um... no, sorry
jim_thompson5910
  • jim_thompson5910
use this unit circle https://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/2000px-Unit_circle_angles_color.svg.png and tell me what angle corresponds to the point with x coordinate \(\Large \frac{\sqrt{3}}{2}\)
jim_thompson5910
  • jim_thompson5910
there are 2 such angles
kittiwitti1
  • kittiwitti1
Okay. I may take awhile, so you don't have to wait (sorry, multitasking) !
jim_thompson5910
  • jim_thompson5910
that's fine
DanJS
  • DanJS
cosine is a function of an angle that angle measure is a function of x, you cant take 4 out
DanJS
  • DanJS
thats 4*an angle, not same as 4*cosine(angle)
kittiwitti1
  • kittiwitti1
I'm still lost...
kittiwitti1
  • kittiwitti1
Wait is it cos(x), find x then div by 2?
DanJS
  • DanJS
\[\cos(\theta) = \frac{ \sqrt{3} }{ 2 }\] is given, and theta, is defined as in terms of an x \[\theta = 2*x\]
kittiwitti1
  • kittiwitti1
so theta/2 to get x
DanJS
  • DanJS
A*sin(B*x) , B changes the period of the wave
kittiwitti1
  • kittiwitti1
Wait what?
kittiwitti1
  • kittiwitti1
What I understood from that: (arcos (sqrt 3 / 2) div by 2
DanJS
  • DanJS
\[\cos(\theta) = \frac{ \sqrt{3} }{ 2 }\] for theta is pi/6, and -pi/6, need both between 0 and 2pi rewrite -pi/6 as 2pi - pi/6 = 5pi/6
kittiwitti1
  • kittiwitti1
Okay...wait why the negative pi/6?
DanJS
  • DanJS
there are the two angles for THeta pi/6 and 5pi/6 theta is a function of x, theta = 2*x so the x values they want are actual x = theta/2
kittiwitti1
  • kittiwitti1
Yes... okay, I get that
DanJS
  • DanJS
half of both those angles, x = pi/12 , x = 5pi/12
kittiwitti1
  • kittiwitti1
Yes
kittiwitti1
  • kittiwitti1
oh so my mistake was the 22pi/12? I got that off Mathway... lol must've mistyped
kittiwitti1
  • kittiwitti1
?
DanJS
  • DanJS
maybe the negative because when you take the inverse of a function that isnt 1-to-1, it wont work. i forget the names of those values , principle angles , or restricted, idk
DanJS
  • DanJS
you have to restrict cosine to angles, or domain from -1 to +1
kittiwitti1
  • kittiwitti1
eh.. okay
DanJS
  • DanJS
think of a reflection over the line y=x, wont work for cos, have to only take a piece from angles 0 to pi, then you can get inverse y=arccos(x) or x = cos(y)
kittiwitti1
  • kittiwitti1
what...?
kittiwitti1
  • kittiwitti1
so 5pi/6 doesn't work?
DanJS
  • DanJS
nvm, if you havent learned about the inverse trig domain and ranges yet
kittiwitti1
  • kittiwitti1
I have actually but I lost you around "reflection" lol
DanJS
  • DanJS
oh, yeah remember finding inverses of algebra functions f^-1 you were told to switch the y and the x around, then solve for y, that is the inverse function
kittiwitti1
  • kittiwitti1
Yeah
DanJS
  • DanJS
same with the trig things, but you have to be careful... y = cos(x) inverse cosine-- x = cos(y), and is same as , y = cos^-1(x)
kittiwitti1
  • kittiwitti1
o-o where does inverse apply here?
DanJS
  • DanJS
but you have to check the domains more careful, trig functions are not 1 to 1 functions, many theta values for any value for cos(theta) because they are periodic and repeat
DanJS
  • DanJS
the thing has to be 1x per 1y value all the time, 1-to-1 function , to do the inverse
kittiwitti1
  • kittiwitti1
??
kittiwitti1
  • kittiwitti1
Ok.
DanJS
  • DanJS
for any x value you pick, only one y can happen, unlike many angles giving same y value for trig things
kittiwitti1
  • kittiwitti1
Actually I need to do other problems, let's just come back to this later
DanJS
  • DanJS
so you limit the domain of cos(theta) to angles 0 to pi, in order to reason the inverse cosine cosine by itself has any number for th edomain
DanJS
  • DanJS
ok, try to reflect cos(x) over the line y = x each point on cos(x) jumps over y=x perpendicularly like a mirror you can only do that if you take cos(x) from just 0 to pi

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