Answer:
The location of the robots hand after rotating 45° counterclockwise from (-20, 0) in inches is (-14.14, 14.14)
The location of the robots hand after rotating 45° clockwise from (-20, 0)) in inches is (-14.14, -14.14)
Step-by-step explanation:
The initial location of the robots hand = (-20, 0)
The angle through which the robot rotates his hand = 45°
∴ We have the length of the robots hand = 20 inches
We note that (-20, 0) is in the 2nd Quadrant
The location of the robots hand after rotating 45° counterclockwise = 135°
Therefore, the location of the robots hand after the rotation = (20×cos(135°), 20×sin(135°)) = (-10·√2, 10·√2) = (-14.14, 14.14)
The location of the robots hand after rotating 45° clockwise from (-20, 0) = 225°
Therefore, the location of the robots hand after the rotation = (20×cos(225°), 20×sin(225°)) = (-10·√2, -10·√2) = (-14.14, -14.14)
