anonymous
  • anonymous
(cos2x)(sinx)=1
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
use the double angle formula for cos2x and get the equation in terms of only sin. you'll have a trig equation in quadraic form.
anonymous
  • anonymous
(1-2sin^2x)(sinx)=1
anonymous
  • anonymous
wow, two problems at once eh? ok, now multiply it out.

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anonymous
  • anonymous
(sinx)-(sin^3x)=1 (sin^3x)-sinx+1
anonymous
  • anonymous
hmm. looks like it's not quadratic. btw. you should have : sinx - 2sin^3x = 1
anonymous
  • anonymous
so we have 2sin^3x - sinx + 1 = 0
anonymous
  • anonymous
yes i just fogot the 2.
anonymous
  • anonymous
|dw:1332976122921:dw| can you factor this?
anonymous
  • anonymous
no.
anonymous
  • anonymous
i think you can but i cant figure the way out.
anonymous
  • anonymous
can u take out an y?
anonymous
  • anonymous
do you know synthetic division? |dw:1332976339846:dw|
anonymous
  • anonymous
so from the synthetic division, (y + 1)*(2y^2 - 2y + 1) = 2y^3 - y + 1
anonymous
  • anonymous
we have to use that. what how come theres a one in the front?
anonymous
  • anonymous
i learned this in like december.
anonymous
  • anonymous
i dont undertsnad where the y+1 came from?
anonymous
  • anonymous
*understand
anonymous
  • anonymous
|dw:1332976636342:dw| the -1 is the root for the factor (y+1)
anonymous
  • anonymous
|dw:1332976678862:dw| and these are the coefficients of 2y^2 - 2y + 1
anonymous
  • anonymous
where did you get the y+1? im sorry i cant understand this.
anonymous
  • anonymous
so now we have: |dw:1332976837183:dw|
anonymous
  • anonymous
ok, remember when you asked "where did that -1 come from?" that is the root of the linear factor of (y + 1)
anonymous
  • anonymous
okay i got it. so now do we put the sin back into the equation
anonymous
  • anonymous
before you do that, notice the quadratic factor does not have real roots... so we can eliminate that...
anonymous
  • anonymous
|dw:1332977231811:dw|
anonymous
  • anonymous
so now you have y+1
anonymous
  • anonymous
right, y + 1 = 0. now you can stick sine back in.
anonymous
  • anonymous
sinx+1=0 sinx=-1 x=270 degree
anonymous
  • anonymous
|dw:1332977538510:dw|
anonymous
  • anonymous
check to see if it is a solution to your equation... |dw:1332977662754:dw|
anonymous
  • anonymous
good work.... :)
anonymous
  • anonymous
thnk u.

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