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 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 −225°, what is the new location of the hand?

Answer 1

(10,0) is on the x-axis, so if you rotate -225°, you are going clockwise 225° which is coterminal with 135°, in the 2nd quadrant
the coordinates would be (10cos135°, 10sin135‚
= (10(-cos45), 10 sin45°)
= (10(-√2/2) , 10(√2/2) )
= ( -5√2 , 5√2 )

Answer 2

(10,0) is 10 units from the origin along the x-axis

negative angles are clockwise rotations
... so the terminal angle is a 45º reference angle in Quad II

x = 10 cos(-225º)

y = 10 sin(-225º)