# Math Help - Tangent Lines

1. ## Tangent Lines

I am stuck on a homework question, any help would be appriciated

Find all points on the curce y=cos(x), ( on the interval 0 greater than or equal to x less than or equal to 2pi), where the tangent line is parallel to the line y=x

2. Originally Posted by Starfire6052
I am stuck on a homework question, any help would be appriciated

Find all points on the curce y=cos(x), ( on the interval 0 greater than or equal to x less than or equal to 2pi), where the tangent line is parallel to the line y=x

So you want all the lines with slope equal to 1 so you want all the points on the curve with

derivative equal to 1 so you want $\displaystyle{y'=-\sin x=1\iff x=\frac{3\pi}{2}\Longrightarrow \left(\frac{3\pi}{2}\,,\,0\right)$ is

the only point.

Tonio