You are given the polar curve $r=\cos(\theta)+\sin(\theta).$

(a) List all of the points $(r,\theta)$ where the tangent line is horizontal. In entering your answer, list the points starting with the smallest value of $r$ and limit yourself to $r \ge 0$ and $0 \le \theta < 2\pi.$ If two or more points share the same value of $r$, list those starting with the smallest value of $\theta.$ If any blanks are unused, type an upper-case "N" in them.

Point 1: $(r,\theta) =$ (,)

Point 2: $(r,\theta) =$ (,)

Point 3: $(r,\theta) =$ (,)

(b) List all of the points $(r,\theta)$ where the tangent line is vertical. In entering your answer, list the points starting with the smallest value of $r$ and limit yourself to $r \ge 0$ and $0 \le \theta < 2\pi.$ If two or more points share the same value of $r$, list those starting with the smallest value of $\theta.$ If any blanks are unused, type an upper-case "N" in them.

Point 1: $(r,\theta) =$ (,)

Point 2: $(r,\theta) =$ (,)

Point 3: $(r,\theta) =$ (,)