Soloving sqrt(5)Cos(2x + 0.464)

  • Thread starter thomas49th
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  • #1
thomas49th
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Homework Statement



Solve for the interval 0 < x < pi/2

[tex]\sqrt{5}Cos(2x+0.464)[/tex]

Homework Equations





The Attempt at a Solution



Am i right in saying as cos oscillate between -1 and 1:

The maximum is sqrt(5) and occurs when (2x-0.464) = 1

Now i got 0.464/2 and (2pi - 0.463)/2
and the back of the book says 0.32 and 2.36

How do you solve equations like above :S

Thanks

yes my calculator is in radians.
 

Answers and Replies

  • #2
nicksauce
Science Advisor
Homework Helper
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FIrst of all, what is it that you are trying to solve?
 
  • #3
thomas49th
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oops i forgot.

solve for x in the range stated above

Thanks ;)
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
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971

Homework Statement



Solve for the interval 0 < x < pi/2

[tex]\sqrt{5}Cos(2x+0.464)[/tex]

Homework Equations





The Attempt at a Solution



Am i right in saying as cos oscillate between -1 and 1:

The maximum is sqrt(5) and occurs when (2x-0.464) = 1

Now i got 0.464/2 and (2pi - 0.463)/2
and the back of the book says 0.32 and 2.36

How do you solve equations like above :S

Thanks

yes my calculator is in radians.
In order to solve any equation, you first have to have an equation. What equation are you talking about. Exactly what is the question you want to answer?

Yes, the maximum of the expression you give is sqrt(5) but it does not occur when 2x+ 0.464= 1, it occurs when 2x+0.464= 0 or a multiplie of 2pi which is, I presume, where you got the values of 0.464/2 and (2pi- 0.463)/2 (it should be -0.464/2= -0.232 and (2pi 0.463)/2). But what is the question to which your book says the answer is 0.32 and 2.36?
 
  • #5
thomas49th
655
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oops i forgot.

solve for x in the range stated above

Thanks ;)
 
  • #6
thomas49th
655
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The rest of the question though is:

I) Express 2Cos2x-Sin2x in the form RCos(2x+a) giving R exactly and a to 3dp
II) Hence find the x-coordinates of the points of interestction of C1 and C2 in the interval 0<=x=<pi. Give your answer as radians and to 2dp

Note that c1 and c2 are curves with the equations y = cos2x - 2sin²x and y = sin2x respectively.
 
  • #7
thomas49th
655
0
it' ok i got it. cos-1(1/sqrt(5))

easy peasy really :)
 

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