anonymous
  • anonymous
Given sinx=1/3 and x is in quadrant 2,find sin x/2and cos x/2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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lochana
  • lochana
you can sinx as \[sinx = 2\sin(\frac{x}{2})\cos(\frac{x}{2})\]
lochana
  • lochana
no. it is not useful here. let's draw 2nd quadrant
lochana
  • lochana
so sinx = sin(pi - x)

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More answers

lochana
  • lochana
sinx = 1/3 x = arcsin(1/3)
lochana
  • lochana
|dw:1447148016922:dw|
anonymous
  • anonymous
the answer is root 12 - root 6 / 6. How do i get there?
lochana
  • lochana
give me one minute
anonymous
  • anonymous
ok
dayakar
  • dayakar
|dw:1447148752743:dw|
dayakar
  • dayakar
sinx = 1/3 given \[\cos x = \frac{ =2\sqrt{2} }{ 3 }\]
dayakar
  • dayakar
\[\sin \frac{ x }{ 2 }=\pm \sqrt{\frac{ 1-\cos x }{ 2 }}\]
dayakar
  • dayakar
substitute cosx value in above u get sin x/2
lochana
  • lochana
@dayakar excellent. can you prove given answers?
dayakar
  • dayakar
@lochana am i right
lochana
  • lochana
yes. you solved it almost completely. but now we need to find sinx/2 and cox/2
dayakar
  • dayakar
let him try ,if he stuck any where we are here to help
dayakar
  • dayakar
\[\cos \frac{ x }{ 2 }=\pm \sqrt{\frac{ 1+\cos x }{ 2 }}\]
lochana
  • lochana
mm.. so get root((3 + root(8))/6) for cosx/2
lochana
  • lochana
that not what he is looking for:(
lochana
  • lochana
ah it is sonx/2 not cosx/2
dayakar
  • dayakar
no,plz observe ,there is only sign difference
lochana
  • lochana
and |dw:1447149934573:dw| it says x exits in 2nd quadrant , that is to say that pi > x > pi/2
lochana
  • lochana
get it?
dayakar
  • dayakar
yes
dayakar
  • dayakar
but we don't get his answer,what he written above
lochana
  • lochana
|dw:1447150474597:dw|
lochana
  • lochana
|dw:1447150660347:dw|
lochana
  • lochana
|dw:1447150691912:dw| now we can find AB distance
lochana
  • lochana
AB^2 = 1^2 + (3- root(8))^2
dayakar
  • dayakar
it becomes too lenthy, just u substitute the cos x value in sin x/2 we get the answer
lochana
  • lochana
\[AB = +or - (6(3 - 8^{1/2}))^{1/2}\]
lochana
  • lochana
we can neglect - value since AB is a distance
lochana
  • lochana
now from the graph sinx/2 = 1/AB cosx/2 = (3-root(8))/AB
lochana
  • lochana
turns out , his answers are not correct :)
lochana
  • lochana
also this is what I did. I drew a rhombus with 3 long each side. because if you draw a line through opposite angle of a rhombus, you divide those angle by 2. meaning you get 2 angles with equal size|dw:1447151308179:dw|
lochana
  • lochana
so that make it easy to get x/2
lochana
  • lochana
hope you are following me
lochana
  • lochana
@dukesmeister please see answers again. and tell me about it. bye
dayakar
  • dayakar
@lochana ur explanation is very good,
lochana
  • lochana
@dayakar it's your idea.

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