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( (x1-x2)^2 + (y1-y2)^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.