# Thread: Polar Curves and Arc Lengths

1. ## Polar Curves and Arc Lengths

Given the polar equation:

r= theta + sin(3theta), theta is greater than or equal to 0 and less than or equal to pi,

Determine the angle which corresponds with the x-coordinate, 3.

OK, so I tried to solve this using the formula such as r^2= x^2 +y^2 ,x=rcos(theta), y=rsin(theta), tan(theta)=y/x ,but I ended up with a really long equation.

Sorry that everything is written out. I don't know how to write the equations using the actual notation.

2. If $(3,y)$ belongs to the curve then,
$\sqrt{9+y^2}=\arctan (y/3)+\sin(\arctan (y/3))$
The left side has absolute value $\geq 3$ and the right side $\leq \pi/2+1<3$ . So, there is no solution.