anonymous
  • anonymous
Evaluate 2sin(pi/3)cos(pi/3)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
@jim_thompson5910 Hii are you busy? Up for any IB SL Math questions tonight?
freckles
  • freckles
you could use unit circle to evaluate both sin(pi/3) and cos(pi/3)
freckles
  • freckles
you could also use the double angle identity and use unit circle once

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anonymous
  • anonymous
Yes, I have it in front of me but I'm confused on what to do
freckles
  • freckles
can you find pi/3 on the unit circle?
anonymous
  • anonymous
yea it's 60 degrees right?
freckles
  • freckles
there should be an ordered pair designated to it
freckles
  • freckles
(x,y)=(cos(),sin())
anonymous
  • anonymous
1/2, sqrt3/2
freckles
  • freckles
so that means the cos(pi/3) is 1/2 and sin(pi/3) is sqrt(3)/2 plug in
anonymous
  • anonymous
ok gimme a sec
anonymous
  • anonymous
ok, just for clarification, what exactly am I doing once I plug them in? I mean am I just dividing, multiplying, etc? By the way, the answer in the back is (0.766, -0.643)
anonymous
  • anonymous
uhh hello..?
freckles
  • freckles
2sin(pi/3)cos(pi/3) is multiplication
freckles
  • freckles
abc means a times b times c
anonymous
  • anonymous
Ohh ok my bad. so i got .037
freckles
  • freckles
how did you get that?
anonymous
  • anonymous
I just plugged into my calculator 2sin(pi/3) * cos(pi/3)
anonymous
  • anonymous
its not right, i know ;-;
freckles
  • freckles
sin(pi/3) is sqrt(3)/2 so replace sin(pi/3) with sqrt(3)/2 cos(pi/3) is 1/2 so replace cos(pi/3) with 1/2 \[2[\sin(\frac{\pi}{3})][\sin(\frac{\pi}{3})] \\ 2[ \frac{\sqrt{3}}{2}][\frac{1}{2}] = \frac{2}{2} [\sqrt{3}][\frac{1}{2}]=....\] you can simplify a little
freckles
  • freckles
oops one of those sin were suppose to read cos
anonymous
  • anonymous
the second one right?
UsukiDoll
  • UsukiDoll
\[2[\sin(\frac{\pi}{3})][\cos(\frac{\pi}{3})] \\ 2[ \frac{\sqrt{3}}{2}][\frac{1}{2}] = \frac{2}{2} [\sqrt{3}][\frac{1}{2}]=....\]
anonymous
  • anonymous
ahh ok so did you get rid of the 2 in the beginning and then add in the 2/2 as a separate thing?
freckles
  • freckles
multiplication is commutative ab =ba
freckles
  • freckles
\[2 \cdot \frac{\sqrt{3}}{2} \cdot \frac{1}{2} \\ =\frac{2}{1} \cdot \frac{\sqrt{3}}{2} \cdot \frac{1}{2} \\ =\frac{2 }{2 } \cdot \frac{\sqrt{3}}{1} \cdot \frac{1}{2}\]
anonymous
  • anonymous
gotcha. But at any rate, I ended up getting 4.71
anonymous
  • anonymous
which, again, doesn't seem right since the answer in the back of the book is totally different
freckles
  • freckles
you do know 2/2=?
anonymous
  • anonymous
1
freckles
  • freckles
right so you have \[\sqrt{3} \cdot \frac{1}{2} \text{ which is just } \frac{\sqrt{3}}{2}\] I don't see how you are getting a number bigger than 1 ...
freckles
  • freckles
since sqrt(3)/2 is definitely less than 1
anonymous
  • anonymous
i think it's just cos im plugging it into my scientific calc then
freckles
  • freckles
ok
anonymous
  • anonymous
oh wait im so dumb i was doing pi3
anonymous
  • anonymous
im so sorry my bad
anonymous
  • anonymous
its .866 right
freckles
  • freckles
yes sqrt(3)/2 is approximately .866
UsukiDoll
  • UsukiDoll
yeah
anonymous
  • anonymous
ok but the answer says it's .766, -0.643
jim_thompson5910
  • jim_thompson5910
@brriiarr the fact that it shows two answers, when it should be one answer, suggests that maybe there's a mixup between the problem and answer
freckles
  • freckles
I don't know what your book is talking about the answer is sqrt(3)/2 which could be written approximately as .866
UsukiDoll
  • UsukiDoll
maybe it's a typo for .766 ???
UsukiDoll
  • UsukiDoll
Ah yes, sometimes there are typos in book. No book is published perfectly. sigh
anonymous
  • anonymous
crap ok. it says in a weird little font next to it sqrt3/2 but i guess you guys were right. umm..do you think i could ask for help on one more?
freckles
  • freckles
you might also want to check the question you type was the question you meant and the answer that correspond to the question you asked was the right correspondence you chose
anonymous
  • anonymous
i think it really was just a typo :p
anonymous
  • anonymous
um but yea I have on more i needed a little help on
anonymous
  • anonymous
ok lol so it's just to find the perimeter and area of the sector. I'll draw it
anonymous
  • anonymous
rty|dw:1449550468325:dw|
anonymous
  • anonymous
ahh so yea, i dunno how to do this at all
anonymous
  • anonymous
umm are any of you guys free or should i just ask another time
jim_thompson5910
  • jim_thompson5910
so this is circle, well a piece of a circle what is the radius of this circle sector? I see 4 but I also see 1^c
anonymous
  • anonymous
it doesnt say
anonymous
  • anonymous
my book says that for theta in radians, the arc length is l=theta*radius but i dunno if that helps
jim_thompson5910
  • jim_thompson5910
so this problem is in your book? or on a computer? if possible, please post what the full problem looks like
anonymous
  • anonymous
here, ill take a pic. gimme a minute.
anonymous
  • anonymous
1 Attachment
jim_thompson5910
  • jim_thompson5910
thanks
jim_thompson5910
  • jim_thompson5910
I'm going to guess that they meant to say \(\LARGE 1^{\circ}\) instead of \(\LARGE 1^c\)
anonymous
  • anonymous
yea it's an aussie book so they write things weird
anonymous
  • anonymous
ah man is this a long one :/
jim_thompson5910
  • jim_thompson5910
oh, I did not know that I'm trying to verify that, but I'm noticing that Australian geometry books also use the degree symbol. So maybe it's only some Australian books?
anonymous
  • anonymous
maaybeee
jim_thompson5910
  • jim_thompson5910
anyways, if it is indeed 1 degree as the central angle, then you'll need to convert 1 degree to radians 1 degree = (1 degree)*(pi radians/180 degrees) = pi/180 = 0.0174532925 radians approximately
jim_thompson5910
  • jim_thompson5910
now that we know 1 degree = 0.0174532925 radians we can use the formula you wrote out L = theta*r L = arc length theta = central angle in radians r = radius
anonymous
  • anonymous
ok one sec lemme write this stuff down
jim_thompson5910
  • jim_thompson5910
to convert from degrees to radians, I used the identity pi radians = 180 degrees
jim_thompson5910
  • jim_thompson5910
and I'm not even thinking, they used the degree symbol just below in set 8B on the same image attachment you posted so it's probably another typo
anonymous
  • anonymous
yes, i understood that. so now what do you multiply? and ugh yea my textbook is horrible honestly i hate it
jim_thompson5910
  • jim_thompson5910
L = theta*r multiply the angle in radians by the radius
anonymous
  • anonymous
i mean, for ex, what's 4 supposed to be?
jim_thompson5910
  • jim_thompson5910
I have a feeling it's not really 1 degree. That just seems too small
anonymous
  • anonymous
wait whats the radius ;-; is that 0.01745...
jim_thompson5910
  • jim_thompson5910
4 looks like the radius
anonymous
  • anonymous
ok right that makes sense. so l=4*0.017453425?
jim_thompson5910
  • jim_thompson5910
yes
anonymous
  • anonymous
kk one sec
anonymous
  • anonymous
so .0698137
anonymous
  • anonymous
lol it says the perimeter = 12 units, area = 8units^2
jim_thompson5910
  • jim_thompson5910
so theta is not really 1 degree
jim_thompson5910
  • jim_thompson5910
maybe theta = 1 radian if so L = theta*r L = 1*4 L = 4
jim_thompson5910
  • jim_thompson5910
curved portion = 4 units straight portions = 2*4 = 8 units
jim_thompson5910
  • jim_thompson5910
I've honestly never seen "1 radian" written as \(\LARGE 1^c\) but maybe that notation is how australians write it
anonymous
  • anonymous
wait so i kinda get it, but why is the curved portion 4 units? i thought the 4 was the radius for the straight line..
jim_thompson5910
  • jim_thompson5910
hmm I learned something new http://image.slidesharecdn.com/pmb05anglesmeasure-151011170600-lva1-app6891/95/pm-b05-angles-measurement-6-638.jpg
anonymous
  • anonymous
ahh cool haha now i know too ^-^
jim_thompson5910
  • jim_thompson5910
because arc length = (angle in radians)*(radius) arc length = (1)*(4) arc length = 4
jim_thompson5910
  • jim_thompson5910
there are 2 sides that are straight and equal to each other |dw:1449552118816:dw|
anonymous
  • anonymous
jesus christ i hate this stupid thing ok so lemme get this straight. L=\[\theta*r\] =4, correct? so then you multiply by 2 cos o f the 2 congruent sides
anonymous
  • anonymous
and then for perimeter, there's 3 sides, the curved, and the two straight lines so therefore it's the arc length^3
anonymous
  • anonymous
so 4*3 = 12 = perimeter
jim_thompson5910
  • jim_thompson5910
yes, the curved side is 4 units long each of the 2 straight sides are 4 units long in total, 4+4+4 = 12
jim_thompson5910
  • jim_thompson5910
it's coincidental how the curved side is equal to the 2 other sides
jim_thompson5910
  • jim_thompson5910
that only happens when the angle is 1 radian
anonymous
  • anonymous
ok, I gotcha. anyway, thank you so much. I wish I could give you the best response :/
jim_thompson5910
  • jim_thompson5910
if you look at the animation on this page https://en.wikipedia.org/wiki/Radian it shows how the radian is set up
anonymous
  • anonymous
thank you! anyway i might be on and off openstudy for a bit. how late do you usually stay? it's 12:30 am eastern time here
anonymous
  • anonymous
im just wondering cos i dont' wanna bother you right when you're about to get to bed lol
jim_thompson5910
  • jim_thompson5910
I've got another hour or so, don't worry
anonymous
  • anonymous
kk, cool. ill probably tag ya later. bye for now!!
jim_thompson5910
  • jim_thompson5910
alright, good luck

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