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.
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.
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.