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Determine all of the solutions in the interval 0< Theta < 360.
cos(Q/2) = 1/2
Q is theta
 one year ago
 one year ago
Determine all of the solutions in the interval 0< Theta < 360. cos(Q/2) = 1/2 Q is theta
 one year ago
 one year ago

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anikayBest ResponseYou've already chosen the best response.0
oh my, beaten to the punch gj
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
haha okay so then hmmm
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
how would that be? @zepdrix i dont get it. i see cos Q/2 that would mean cos = 1/2 right? and if its positive it would be in the 1st and 4th Quadrant?
 one year ago

anikayBest ResponseYou've already chosen the best response.0
well, now that I think about it, I think raja might be wrong
 one year ago

anikayBest ResponseYou've already chosen the best response.0
it should have 4 solutions right?
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
im not sure, it just says to determine all solutions in the interval 0>360
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Using Q? Oooo I like that :) I'm always having trouble finding a suitable letter for theta in text, that works quite well XD
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
lol ya, i got tired ofputting theata.
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
okay is it 60 and 300 degrees?
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
\[\large \cos(\theta/2)=\frac{1}{2}\]We need to solve for theta, which involves a little more than just finding a special angle. If it helps, think of the ENTIRE inside of cosine as an angle, like this,\[\large \cos(\phi)=\frac{1}{2}\]Where is phi =1/2? Which special angles?
 one year ago

anikayBest ResponseYou've already chosen the best response.0
look, as I solve it, it's \[\theta=2\cos^{1} (1/2)\]
 one year ago

anikayBest ResponseYou've already chosen the best response.0
the thing is, that only gives you 120. but it's a good starting point
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
mmmmm... okay, well first. special angles is like 454590, and 306090, right?
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
The special angles are 0,30, 45, 60, 90 In radians 0, pi/6, pi/4, pi/3, pi/2 and so on... Remember those? :) We're not talking about special triangles :D Special angles on the unit circle.
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
oh....okay i gotcha now on special angles. lol im totaly flipped around in this class
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
okay then so..cosQ/2 = 1/2 right? so cos would be a positive
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
yes the cosine is producing a positive value, so we're concerned with angles in the 1st and 4th quadrant right? :O Cuz that's where cosine is positive.
 one year ago

anikayBest ResponseYou've already chosen the best response.0
so, if we find the reference angle, then what would the two angles be?
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
mmm....pi/3 and 5pi/6?
 one year ago

anikayBest ResponseYou've already chosen the best response.0
yes to the first, the last, not so much, that's in the second quadrant
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
lol :) They should both either be /6 or /3 :D you should get similar angles in that sense. Also, the domain of theta was given to us in DEGREES. let's try to keep it in degrees :)
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
oh. haha i mean 5pi/3
 one year ago

anikayBest ResponseYou've already chosen the best response.0
With zepdrix, but you are right
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
so the second answer would be 5pi/3?
 one year ago

anikayBest ResponseYou've already chosen the best response.0
but, the problem is, we need that angle to be doubled to match our equation of theta/2
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
hmmm...ok okkay, so doubled from pi/3, so pi/3 and 5pi/6?
 one year ago

anikayBest ResponseYou've already chosen the best response.0
uh, lets throw this back to degrees shall we? pi/3 = 60 and 5pi/3 = 300
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
DANG! haha okay, so first we have 60 and u said to double it, so that would be 120, 120 would be.....that 5pi/6
 one year ago

anikayBest ResponseYou've already chosen the best response.0
no, 5pi/6 = 150 degrees
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
haha shoot what am i doing wrong
 one year ago

anikayBest ResponseYou've already chosen the best response.0
here's a tip. every pi/6 = 30 degrees
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
pi/6 pi/4 pi/3 pi/2 4pi/6div by 2 = 2pi/3 OH!.....haha okay so pi/3 and 2 pi/3???
 one year ago

anikayBest ResponseYou've already chosen the best response.0
just plug those into your original equation and see what you get :P
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
i dont have an equatioN haha says determine all of the solutions in the interval 0< Q<360 cos(Q/2) = 1/2 so the answers would be pi/3 and 2pi/3? right?
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
@zepdrix is it pi/3 and 2pi/3?
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
If the problem had been,\[\large \cos\left(\theta\right)=\frac{1}{2}\]We would have concluded that,\[\large \theta=\quad 60^o,\quad 300^o\] But our problem involved Q/2, not Q. Giving us,\[\large \cos\left(\frac{\theta}{2}\right)=\frac{1}{2}\] \[\frac{\theta}{2}=\quad 60^o,\quad 300^o\] From here, if we multiply both sides by 2, we can solve for Q.
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
I'm a little confused why you're messing with the radians :C They're a little more confusing to work with. The domain of Q was GIVEN to us in DEGREES. So let's work in degrees! :D
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
AH! so i was right?! the 60 and 300?!
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
\[\large \theta=\quad 120^o, \quad 600^o\]
 one year ago

anikayBest ResponseYou've already chosen the best response.0
and since we're going only to 360?
 one year ago

anikayBest ResponseYou've already chosen the best response.0
(radians are easier imo but degrees work k)
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
AH!!! im so lost haha
 one year ago

anikayBest ResponseYou've already chosen the best response.0
its almost like you're my lilsis or somethin xD
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
okay so i get the 1/2 and that is in the first quad giving me 60 degrees right?
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
okay, how can i figure out the 300?!
 one year ago

anikayBest ResponseYou've already chosen the best response.0
it's a reference angle of 60
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
yes it is a ref angle 60
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
WAIT!!! 300 cuz its cos 1.2, sin  sqrt3 /2 ?!
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
right?! dang i think im slow
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
haha did i do it right?!
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
YAY!!!! > . < THANK YOU SO MUCH!!! ugh....
 one year ago

anikayBest ResponseYou've already chosen the best response.0
however, you have to double those and since you only go to 360, 120 is your only answer
 one year ago

phiBest ResponseYou've already chosen the best response.1
sometimes sketching the curve is helpful dw:1355239813847:dw
 one year ago

anikayBest ResponseYou've already chosen the best response.0
agreed, but my calculator is dead xD
 one year ago
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