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# P2 watch

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1. Solve the equation..

cos x - (rt3)sin x = rt2

between 0 and 360.
2. (Original post by jonnymcc2003)
Solve the equation..

cos x - (rt3)sin x = rt2

between 0 and 360.

Whats rt3 and rt2?
3. (Original post by BlueAngel)
Whats rt3 and rt2?
square root
4. (Original post by BlueAngel)
Whats rt3 and rt2?
Square root of 2 etc
5. (Original post by jonnymcc2003)
Solve the equation..

cos x - (rt3)sin x = rt2

between 0 and 360.

Thats a hard one that.
rt3/2 is Sin 60 or Cos 30

Oh I dont know.
6. I get there is no solution...so I think I might have done it wrong lol

but what I basically did is put the sin on the other side, then square both sides, then make cos^2x = 1-sin^2x so now you've only got sin^2x's sinx's and units, so you've got a quadratic, then make a substituion of u=sin x and solve
7. i dunno if there are more solutions, but you get the idea
8. Same method as katie heskins

CosX - √3SinX = √2
CosX = √2 + √3Sinx
Cos²X = 2 + 2√6Sinx + Sin²X
(1 - Sin²X) = 2 + 2√6Sinx + Sin²X
2Sin²X + 2√6Sinx + 1 = 0

Then solve using the quadratic formula.

I got sinX = -0.225 or nothing as the other answer gives an answer smaller than -1.

So X = 347 or 193.0

don't know if it's right though.
9. hmm

i used rcos(theta + alpha)

r=root(1+3)=2

alpha = tan^-1(-root3/1)

so you get

2cos(theta-60)=root(2)

etc
10. For a P2 student I daresay Kitzens method is the one that the exam board would have in mind.
11. Just to add to Kikzens solution. There of course is a second solution. Remember that cosx = cos(-x), so
cos(x+60) = 1/sqrt(2)
x+60 = 45, -45

Gives, x = 255 and 345.
12. Also, Katie and Mysticisms method works, but only finds one solution. Because you have squared, you get another solution which will not work.

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Updated: June 14, 2004
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