Question

Find a number x0 between 0 and pi such that the tangent line to the curve y = sin x at x = x0
is parallel to the line y = -x=2.

I get that for both lines to be parallel to each other their slopes need to be the same.

I found -1/2 = cos(x) but I get stuck here. What exactly am I supposed to do? Use special triangles?

Answer 1

all you have to do is solve cos(x) = -1/2
You know that cos pi/3 = 1/2 (so I guess that means using special triangles), and that cos(x) < 0 in QII and QIII.

So, x = 2pi/3, since we are in QII.

If you got a slope of -1/2, then the line must have been y = -x/2. That doesn't look like what you have, but you can easily fix it.