Question

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Answer 1

do you want the slope as dy/dx?

Answer 2

A couple ways to do it.
you can find dx/dy then invert it, or solve for y then find derivative of arccos(x).

Answer 3

Either way, it helps to draw the right triangle and label the sides and angles according to the situation.
e.g.

Answer 4

I got something different, but I'll double check it.
It says x = cos(y) and y=-π/3, so use that to find x first, 'cause we'll need it later.
What did you get for x?

Answer 5

Right. So you can find dx/dy first, then invert it.

Answer 6

dx/dy is the derivative of cos(y). Take the reciprocal of that derivative to get dy/dx then use that triangle I drew to put it in terms of x.

Answer 7

How did you get that?

Answer 8

Ah, ok, don't plug in that value of x until the end; need to get the derivative function first.
The derivative of cos(y) is -sin(y). That is dx/dy, so to get dy/dx, flip that upside down to -csc(y).

Answer 9

just missing a negative sign in front.