what is (x, y) equal to?

Question

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 20 inches long that can rotate about the origin in a coordinate plane. If the robot's hand is located at (20, 0) and then rotates through an angle of -135° what is the new location of the hand? Enter an exact (simplified) answer with no trigonometric functions.

 

(x, y)= 

Answer 1

 

The new position of the robot hand will be:

 

    (x, y) = (20cos(-135º), 20sin(-135º)) = (-20(√2/2), -20(√2/2)) = (-10√2, -10√2)

 

A negative angle of rotation is, by convention, one that is clockwise.  If the positive y-axis is taken to be "north" then the robot arm will be pointing south-west after the -135º rotation.