Finding the radius, solving, and finding theta?

**#1 In a circle, an arc of length 30 cm contains a central angle of 120 degrees. Determine the radius of this circle.**

Work: 30/(2(pi)r) = (3pi/4)/2pi

r= 40/pi... But this isn't right.

**Answer:** 45/pi

**#2 Solve: 5(sin(x))^2 = cos(x)**

Work: Unsure how to start this and finish it. I also tried graphing it and finding the intersections, but I got HUGE numbers (3 digit range).

**Answer:** 0.44, 5.84

#3 The point (5, -6) is on the terminal arm of the standard position angle theta. Determine the smallest positive measure of theta in radians.

Work: graphed coordinates (5, -6), but don't know how to continue.

**Answer:** 5.41