The unit circle, and exact trig values of the special angles

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   Ren's robot turns θ counterclockwise from (1, 0) on a unit circle floor grid and stops at (-√3/2, 1/2). Which angle θ, from 0 to 2π, is it?

   • 5π/3
   • 7π/6
   • 5π/6
   • π/6
2. 2.

   Tala marks the point (-√3/2, -1/2) on a unit circle worksheet. Which angle θ, from 0 to 2π, ends at this point?

   • 7π/6
   • 5π/6
   • 4π/3
   • π/6
3. 3.

   Zee's robot turns θ counterclockwise from (1, 0) on a unit circle floor grid and stops at (1/2, -√3/2). Which angle θ, from 0 to 2π, is it?

   • π/3
   • 5π/6
   • 2π/3
   • 5π/3
4. 4.

   Esme marks the point (-1/2, -√3/2) on a unit circle worksheet. Which angle θ, from 0 to 2π, ends at this point?

   • 4π/3
   • 7π/6
   • 2π/3
   • π/3
5. 5.

   Jun's math book shows that 60° ends at (1/2, √3/2). Where on the unit circle does a turn of 240° end?

   • (-1/2, -√3/2)
   • (-√3/2, -1/2)
   • (-1/2, √3/2)
   • (1/2, √3/2)
6. 6.

   Kira's worksheet shows that 60° ends at (1/2, √3/2). Where on the unit circle does a turn of 120° end?

   • (√3/2, -1/2)
   • (1/2, √3/2)
   • (-1/2, -√3/2)
   • (-1/2, √3/2)
7. 7.

   Luz's math book shows that 30° ends at (√3/2, 1/2). Where on the unit circle does a turn of 330° end?

   • (√3/2, 1/2)
   • (√3/2, -1/2)
   • (-√3/2, -1/2)
   • (-1/2, √3/2)
8. 8.

   Milo's worksheet shows that π/6 ends at (√3/2, 1/2). Where on the unit circle does a turn of 7π/6 end?

   • (-1/2, -√3/2)
   • (-√3/2, 1/2)
   • (√3/2, 1/2)
   • (-√3/2, -1/2)
9. 9.

   Noah works out sin 60° × cos 30° on a unit circle worksheet. What is the exact product?

   3/4
10. 10.

    Ren works out cos(π/4) × sin(π/4) on a unit circle worksheet. What is the exact product?

    1/2