Angles in standard position: quadrants, coterminal and reference angles

Answer Key - Grade 11 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   Milo's robot spins 1110° counterclockwise from the positive x-axis. Which angle from 0° to 360° names where the robot stops?

   30
2. 2.

   Ren's robot spins 1040° clockwise from the positive x-axis. Which angle from 0° to 360° names where the robot stops?

   40
3. 3.

   Tala writes a rule for every angle coterminal with 130°, where k is any integer. Which rule is right?

   • 130° + 2πk
   • 130° + 180°k
   • 130° + 90°k
   • 130° + 360°k
4. 4.

   Zee's math book asks for every angle coterminal with -45°, where k is any integer. Which rule is right?

   • -45° + 90°k
   • -45° + 360°k
   • -45° + 180°k
   • -45° + 2πk
5. 5.

   Esme writes a rule for every angle coterminal with 5π/4 radians, where k is any integer. Which rule is right?

   • 5π/4 + (π/2)k
   • 5π/4 + πk
   • 5π/4 + 360k
   • 5π/4 + 2πk
6. 6.

   Jun's math book asks for every angle coterminal with -π/3 radians, where k is any integer. Which rule is right?

   • -π/3 + (π/2)k
   • -π/3 + 360k
   • -π/3 + πk
   • -π/3 + 2πk
7. 7.

   Kira's robot turns -7π/6 radians, clockwise from the positive x-axis. What is the reference angle of the turn, in radians?

   π/6
8. 8.

   Luz's bike wheel turns 10π/3 radians from the positive x-axis. What is the reference angle of the turn, in radians?

   π/3
9. 9.

   Milo spins a spinner arrow 19π/6 radians from the positive x-axis. What is the reference angle of the turn, in radians?

   π/6
10. 10.

    Noah turns a clock hand -2π/3 radians, clockwise from the positive x-axis. What is the reference angle, in radians?

    π/3