Points on the terminal sides of angles play an important part in the design of arms for robots.

Question

Suppose a robot has a straight arm 10 inches long that can rotate about the origin in a coordinate plane. If the robot's hand is located at (10, 0) and then rotates through an angle of −60°, what is the new location of the hand? (Round your answers to two decimal places.)

Answer 1

Draw a diagram and label:

 

The new point is (x, y). The hypotenuse is 10 (the length of the robot's arm).

sin 60° = y/10                  now solve for y.

cos 60° = x/10                  now solve for x