Help with advanced math problems? Please 2 problems?

Question

1. Rewrite the square root of cos^2 + sin ^2 +cot^2 in a nonradical form without using absoulte values for pi
2. Points on the terminal sides of angles play an important part in the design of arms for robots. Suppose a robot has a straight arm 18 in. long that can rotate about the origin in a coordinate plane. If the robot's hand is located at (18,0) and then rotates through an angle of 60 degrees, what is the new location of the hand....??? this one is really confusing me..

I tried these a few times already and need some help. It would be greatly appreciated :)

Answer 1

√(cos² + sin² + cot²) =
√(1 + cot²) =
√csc² =
csc

draw a right triangle in quad 1, base on x axis, hypotenuse of 18 making 60° angle with x axis. from geometry you know base is 9, vertical side is 9√3, so location of hand is (9, 9√3).