Gradient of stationary points

  • Thread starter pip_beard
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  • #1
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Homework Statement


gradient of the stationary points of y=1-2sinx domain 0<x<2pi


Homework Equations





The Attempt at a Solution


dy/dx = -2cosx
-2cosx=0......?
 
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Answers and Replies

  • #2
rock.freak667
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Gradient of the stationary point? Do you need to find that or the gradient? Because when you put dy/dx=0 it sort of implies what the gradient will be.
 
  • #3
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Gradient of the stationary point? Do you need to find that or the gradient? Because when you put dy/dx=0 it sort of implies what the gradient will be.

Sorry. the qu reads 'the curve y=1-2sinx has domain 0<x<pi. find the gradients of the curve at the points where the curve crosses the x-axis
 
  • #4
rock.freak667
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Sorry. the qu reads 'the curve y=1-2sinx has domain 0<x<pi. find the gradients of the curve at the points where the curve crosses the x-axis

Ah that is different.

Well you know the gradient function is dy/dx.

You need to find when the curve crosses the x-axis, or when y=0.
 
  • #5
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so do i differentiate it and make it = 0?

so i get -2cosx=0
 
  • #6
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so do i differentiate it and make it = 0?

so i get -2cosx=0

how to i rearrange this to work it out?
 
  • #7
rock.freak667
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so do i differentiate it and make it = 0?

so i get -2cosx=0

how to i rearrange this to work it out?

No if y=1-2sinx, the curve crosses, the x-axis when y=0

so solve 1-2sinx=0 for x. Can you do that?
 
  • #8
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-2sinx=1
sinx=-1/2
 
  • #9
rock.freak667
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-2sinx=1
sinx=-1/2

which gives x as ? ( in the given domain that is)
 
  • #10
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principle value of -0.523 (but out of range) the pi-(-0.523) = 3.6651

therfore value = 3.6651 and 6.2832?????
 
  • #11
rock.freak667
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-2sinx=1
sinx=-1/2

principle value of -0.523 (but out of range) the pi-(-0.523) = 3.6651

therfore value = 3.6651 and 6.2832?????



this should be sinx=1/2.


But how did you get that value for x?
 
  • #12
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ohhh... did sin^-1... so ....

x principle = 0.479425
so pi - 0.4879425 = 2.66216
 
  • #13
rock.freak667
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ohhh... did sin^-1... so ....

x principle = 0.479425
so pi - 0.4879425 = 2.66216

you should get x= π/6 and another one, best to use the exact values, I don't have a calculator with me to divide out pi.
 
  • #14
14
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ok. i'll have a play and post back if i cant do it.. Thanks for the inspiration!
 

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