Finding the Gradient of Stationary Points in Trigonometric Functions

[pip_beard]

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...?

 

[rock.freak667]

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.

 

[pip_beard]

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

 

[rock.freak667]

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.

 

[pip_beard]

so do i differentiate it and make it = 0?

so i get -2cosx=0

 

[pip_beard]

so do i differentiate it and make it = 0?

so i get -2cosx=0

how to i rearrange this to work it out?

 

[rock.freak667]

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?

 

[pip_beard]

-2sinx=1
sinx=-1/2

 

[rock.freak667]

-2sinx=1
sinx=-1/2

which gives x as ? ( in the given domain that is)

 

[pip_beard]

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

therfore value = 3.6651 and 6.2832?

 

[rock.freak667]

-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?

 

[pip_beard]

ohhh... did sin^-1... so ...

x principle = 0.479425
so pi - 0.4879425 = 2.66216

 

[rock.freak667]

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.

 

[pip_beard]

ok. i'll have a play and post back if i can't do it.. Thanks for the inspiration!