(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the point on the curve y = cos (x) closest to the point (1,1)

2. Relevant equations

Tangent line equation

y = f'(c)(x-c)+f(c)

Distance formula

d = SQRT( (x_{1}-x_{2})^2 + (y_{1}-y_{2})^2 )

3. 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.

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# Homework Help: Find the point on a curve that is closest to the point (1,1), unsure how to continue

**Physics Forums | Science Articles, Homework Help, Discussion**