anonymous
  • anonymous
if trying to find all solutions on the interval 0,2pi sin2x=sinx so x=1/2? or how do i solve?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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myininaya
  • myininaya
sin2x=2sinxcosx so 2sinxcosx=sinx 2sinxcosx-sinx=0 sinx(2cosx-1)=0 sinx=0 and 2cosx-1=0
myininaya
  • myininaya
lets solve sinx=0 first
myininaya
  • myininaya
what x makes sinx zero

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myininaya
  • myininaya
think about your unit circle
myininaya
  • myininaya
sin(0) is what?
anonymous
  • anonymous
0 or pi
myininaya
  • myininaya
sin(0)=0 sin(2pi)=0 so x=0 and 2pi now we have the other equation 2cosx-1=0 => cosx=1/2
myininaya
  • myininaya
what can plug in where the x is that give you 1/2 (we are looking at the equation cosx=1/2)
anonymous
  • anonymous
60 degrees
anonymous
  • anonymous
the other btw was 0 degrees or 180 degrees for sin
myininaya
  • myininaya
oh yes and pi very good for the first
anonymous
  • anonymous
so answeres are 0,1/2,pi?
myininaya
  • myininaya
so 60 degrees and what else for this equation equation
myininaya
  • myininaya
no not 1/2
myininaya
  • myininaya
60 degrees or pi/3 there is also another one for the second equation
anonymous
  • anonymous
ah
anonymous
  • anonymous
0,pi/3,pi that seems like all we can get i think cause thats both sin and hte one cos
anonymous
  • anonymous
@myininaya: Congrats for the new title. I was you 100th fan by the way :D
anonymous
  • anonymous
i was 99th XD
myininaya
  • myininaya
thanks lol
myininaya
  • myininaya
so anyways what is cos(300 degrees)
anonymous
  • anonymous
10pi/6
myininaya
  • myininaya
no maybe it will help if i wrote it in radians what is cos(5pi/3)
anonymous
  • anonymous
isnt that the same just reduced?
myininaya
  • myininaya
ok 10pi/6=5pi/3 but what is cos(5pi/3)
myininaya
  • myininaya
=1/2
anonymous
  • anonymous
-1/2?
anonymous
  • anonymous
isnt it - cause bottom right quadrent?
anonymous
  • anonymous
nvm cos is x so positive if on right side
myininaya
  • myininaya
k :) so the solutions to sinx=0 in the interval [0,2pi] are 0,pi,2pi and the solutions to cosx=1/2 in the interval [0,2pi] are pi/3, 5pi/3
myininaya
  • myininaya
you have 5 solutions in all
anonymous
  • anonymous
thank you
myininaya
  • myininaya
np

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