# maths question - for rep

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16 years ago
#21
(Original post by happysunshine)
Is this from Maths/Further Maths A-Level?
Just Maths A Level.
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16 years ago
#22
(Original post by ShOcKzZ)
solve, for 0<x<2pi

2sinXcos2X + sin2X = 0

thanks
2sinxcos2x + sin2x = 0

2sinXcos2X + 2sinXcosX = 0

2(sinXcos2X + sinXCosX) = 0

sinXcos2X + sinXcosX = 0

so, the solution are the x values when sinXcos2X = -sinXcosX

0, pi/3, pi, 5pi/3, 2pi

(I have checked answers on a graphic calculator and i'm as sure as i can be that they're right)
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16 years ago
#23
i did it this way....

sin2X = 2SinxCosx

so.. 2sinXcos2X + 2SinxCosx = 0

= 2Sinx ( cos2x + cos x) = 0

since you are finding solutions for = 0, you just needed to solve each factor to 0....

2Sinx = 0 @ 0 & 2pi

cos 2x + cos x = 0

written as..... cos2x = - cos x

with solutions at x = pi/3 , pi, 5 pi/3

therefore total soultions between 0 and 2 pi are...

0, pi/3, pi, 5 pi/3, 2 pi ...... i think 0
16 years ago
#24
(Original post by Mysticmin)
Right, here goes...

2sinXcos2X + sin2X = 0
2SinX(Cos^2X - Sin^2X) + 2SinxCosX=0
2SinX(Cos^2X - Sin^2X + CosX) = 0
2SinX(Cos^2X - (1- Cos^2X) + CosX) = 0
2SinX(2Cos^2X + CosX -1) = 0
2SinX(2CosX + 1)(CosX - 1) = 0

SinX = 0 --> X = 0, 180, 360
CosX = 1 --> X = 0 or 360.
CosX = -1/2 ---> X = 120, 240.

answers: 0, 120, 180, 240, 360.
or in radians: 0, 2pi/3, pi, 4pi/3, 2pi.

did that work out right? Someone check my algebra...i make silly mistakes often.
yeah thats exactly right, except for its 5pi/3 not 4pi/3, all your working is correct so it's probably just a typo.
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16 years ago
#25
(Original post by iiikewldude)
yeah thats exactly right, except for its 5pi/3 not 4pi/3, all your working is correct so it's probably just a typo.
wouldn't 5pi/3 made 300 degrees? and cosine 300 is positive.
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16 years ago
#26
(Original post by Turnip09)
Ralfskini is wrong.

dont be startled its an easy error-

it works out at 2cosx= 1/2

and therefore sin^2-cos= 1/2

factorise from here and bob's your uncles brother.

I think you should check your maths. Im pretty sure mine is right.
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16 years ago
#27

ta !
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