anonymous
  • anonymous
can someone please help me! please! i have a test in an hour!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
for sin3x = 1/2 why is the answer pi/18 and 5pi/18 ?
anonymous
  • anonymous
That is not a math question. This might be better suited for chat.
apoorvk
  • apoorvk
first thing. dont panic. we ll help you but this last minute thing wont help you now. what ll help you is staying calm to focus your mind and use you intelligence. have confidence mate, it wont be so bad (never is)!!! :)))

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More answers

anonymous
  • anonymous
start with \[\sin(3x)=\frac{1}{2}\] now forget about the 3x for a moment, just figure out what angle (number) as sine of 1/2 if you are working in degrees, on such angle is 30 in radians it is \[\frac{\pi}{6}\]
anonymous
  • anonymous
so you have \[3x=\frac{\pi}{6}\] and so \[x=\frac{\pi}{18}\] is one possible answer
anonymous
  • anonymous
where do you get the pi over 6?
anonymous
  • anonymous
ok so now for some of these there are more than one solution (because they can be in different quadrants) how do you know which quadrant?
anonymous
  • anonymous
it is also true that \[\sin(\frac{5\pi}{6})=\frac{1}{2}\] and so \[3x=\frac{5\pi}{6}\] therefore \[x=\frac{5\pi}{18}\]
anonymous
  • anonymous
are you asking how i know that \[\sin(\frac{\pi}{6})=\frac{1}{2}\]?
anonymous
  • anonymous
mmm i don't think so I'm asking like
anonymous
  • anonymous
if i have sin 3x = 1/2 why are there 2 answers?
anonymous
  • anonymous
look at the last page of the attached cheat sheet. sine is the second coordinate so find the places on the unit circle where the second coordinate is 1/2
anonymous
  • anonymous
there are not two answers, there are an infinite number of answers because sine is periodic. so there are an infinite number of numbers whose sine is 1/2
anonymous
  • anonymous
i just gave an example of two of them
anonymous
  • anonymous
hmmm so if i had 4 sinx + 3 = 1
anonymous
  • anonymous
i would first do 4 sinx = -2 so sinx = -1/2
anonymous
  • anonymous
start with \[\sin(x)=-\frac{1}{2}\]
anonymous
  • anonymous
since sin is y/R then would it be in quadrant III and IV because thats where y value is negative?
anonymous
  • anonymous
then look on the unit circle for the angles where the second coordinate is -1/2
anonymous
  • anonymous
oh i see! so hmmmmm what if i had tan = -3 /4
anonymous
  • anonymous
you will see two possibilities, \[\frac{7\pi}{6}\]or \[\frac{11\pi}{6}\]
anonymous
  • anonymous
how do i do that because i don't know if the 3 (y) or the 4 (x) is negative
anonymous
  • anonymous
if you have \[\tan(x)=-\frac{3}{4}\] you will need a calculator
anonymous
  • anonymous
how do i know if the y or x value is negative?
anonymous
  • anonymous
need to use \[x=\tan^{-1}(-\frac{3}{4})\]
anonymous
  • anonymous
you don't
anonymous
  • anonymous
you could either be in quadrant II or IV
anonymous
  • anonymous
hmmmm.. why those quadrants?
anonymous
  • anonymous
because in quad II sine is positive but cosine is negative, so tangent will be negative in quad IV sine is negative and cosine is positive, so tangent will be negative
anonymous
  • anonymous
ohh! that makes a lot of sense. do you think you could give me a few problems to try? like just 2 or 3?
anonymous
  • anonymous
\[2\sin(2x)=\sqrt{3}\]
anonymous
  • anonymous
\[\sqrt{3}\tan(x)=1\]
anonymous
  • anonymous
lets see x = sqrt 3 y = 1 and r = 2
anonymous
  • anonymous
now this must be in quadrant 1 or 3 since x and y are positive (they could both pbe positive or both be negative)
anonymous
  • anonymous
30 degress or 210 degres
anonymous
  • anonymous
that is rigth for the first one!
anonymous
  • anonymous
:DDDDD
anonymous
  • anonymous
how would you do 3 - sinx = 2sin x?

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