- #1
Knight226
- 16
- 0
Homework Statement
Find the point on the curve y = cos (x) closest to the point (1,1)
Homework Equations
Tangent line equation
y = f'(c)(x-c)+f(c)
Distance formula
d = SQRT( (x1-x2)^2 + (y1-y2)^2 )
The Attempt at a Solution
I have problem doing the f'(c) part. I get stuck when I have trigonometry in the equation where I have to set it to zero to find the critical number...
So far I have
d = SQRT( (x-1)^2 + (y-1)^2 )
y = cos (x)
d = SQRT( (x-1)^2 + (cos(x)-1)^2 )
*Here according to my textbook, what matter is what is inside radical sign*
f(x) = (x-1)^2 + (cos(x)-1)^2
f(x) = x^2-2x+2+cos^2x-2cosx
f'(x) = 2x - 2 - sin2x + 2sinx
Set f'(x) to zero
2x - 2 - sin2x + 2sinx = 0
Get stuck here :(
let say I do...
-sin2x + 2sinx = -2x + 2
then.. I don't know what to do next... I am horrible with trigonometry... Please help. Thank you very much in advance. Please let me know if I have made mistakes somewhere along the calculation.