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## Homework Statement

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.

## Homework 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.

## 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)/x

^{2}+ y’(siny)(-y

^{-2}) + cosy(y’)(y

^{-1}) = 0

which I THINK can be simplified to:

((x)(cosx) – sinx)/x

^{2}+ 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)/x

^{2}= -y’(siny*-y

^{-2}+ cosy*y

^{-1})

-((((x)(cosx) - sinx)/x

^{2})/(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.

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