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How do I find the coordinates of the points on the curve y = (2-cos(x)) / sin(x) , in...

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nicoleuc | Student, Undergraduate | eNoter

Posted October 9, 2011 at 5:43 PM via web

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How do I find the coordinates of the points on the curve y = (2-cos(x)) / sin(x) , in the range 0<x<2pi , where the gradient is 3/8.

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted October 10, 2011 at 12:11 AM (Answer #1)

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(2-cos(x))/sinx

==> y' =sinx -(2-cosx)cosx)/sin^2 x

==> (sin^x -2cosx+cos^2 x)/sin^2 x

==> (1-2cosx)/sin^2 x

==> (1-2cosx)/sin^2 x = 3/8

==> 8(1-2cosx) = 3sin^2 x

==> 8 - 16cosx = 3-3cos^2 x

==> 3cos^2 x -16cosx +5 = 0

==. (3cosx -1)(cosx -5) = 0

==> (3cosx-1)= 0 ==> cosx = 1/3 ==> x=70.5

==> cosx-5 = 0 ==> cosx = 5 ( Invalid)

==> x= 70.5 degrees.

==> y= (2-cosx)/sinx = (2- 1/3)/ (0.94)= 1.77

==>Then the point (x,y)= (70.5, 1.77) such that the gradient is 3/8.

 

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