1. The problem statement, all variables and given/known data Suppose the point (pi/3, pi/4) is on the curve sinx/x + siny/y = C, where C is a constant. Use the tangent line approximation to find the y-coordinate of the point on the curve with x-coordinate pi/3 + pi/180. 2. Relevant equations TLA: f(a) + f'(a)(x-a) Where a is the known value of x and x is the value you are estimating the output of. 3. The attempt at a solution Before differentiating I figured that I could replace siny/y with siny * y^-1. I got here: ((x)(cosx) – sinx)/x2 + y’(siny)(-y-2) + cosy(y’)(y-1) = 0 which I THINK can be simplified to: ((x)(cosx) – sinx)/x2 + y’(siny*-y-2 + cosy*y-1) dunno where to go with it from there D: MAYBE, here's what I attempted: ((x)(cosx) - sinx)/x2 = -y’(siny*-y-2 + cosy*y-1) -((((x)(cosx) - sinx)/x2)/(siny*-y-2 + cosy*y-1)) = y' But that doesn't seem right. The question gave the curve sinx/x + siny/y = C with the point (pi/3, pi/4) given. Substituting I got C = 1.7273097. However using tangent line approximation with the derivative I calculated I got the y coordinate there to be 418.879: f(a) + f’(a)(x – a) f(π/3) + f’(π/3)(π/180) 1.7273097 + 24000(π/180) I know I could just do normal algebra for this instead of calculus but the instructions say to use tangent line approximation so I think I'd get points docked. I am pretty sure though the answer I'm after is y = 0.905801 based on just solving for the values using C = 1.7273097 and x = pi/3 + pi/180... pretty far off from 418.879. Someone please help, I've got no idea what to do here. If it helps get the help any quicker I don't really care about a pretty, formatted answer... I really need help on this soon so whatever helps.