Trig values by reference angle and quadrant sign, and the reciprocal ratios

Answer Key - Grade 11 Math Worksheet - Building Confidence

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

1. 1.

   Pia turns a spinner arrow 140° from the positive x-axis, ending at the point (cos θ, sin θ). Which signs do cos θ and sin θ have?

   • cos θ < 0 and sin θ > 0
   • cos θ < 0 and sin θ < 0
   • cos θ > 0 and sin θ > 0
   • cos θ > 0 and sin θ < 0
2. 2.

   Ren's robot turns 320° counterclockwise on a unit circle floor grid, ending at (cos θ, sin θ). Which signs do cos θ and sin θ have?

   • cos θ < 0 and sin θ < 0
   • cos θ > 0 and sin θ < 0
   • cos θ > 0 and sin θ > 0
   • cos θ < 0 and sin θ > 0
3. 3.

   Tala turns a spinner arrow 250° from the positive x-axis, ending at the point (cos θ, sin θ). Which signs do cos θ and sin θ have?

   • cos θ > 0 and sin θ < 0
   • cos θ < 0 and sin θ < 0
   • cos θ < 0 and sin θ > 0
   • cos θ > 0 and sin θ > 0
4. 4.

   Zee's robot turns 100° counterclockwise on a unit circle floor grid, ending at (cos θ, sin θ). Which signs do cos θ and sin θ have?

   • cos θ > 0 and sin θ > 0
   • cos θ < 0 and sin θ < 0
   • cos θ < 0 and sin θ > 0
   • cos θ > 0 and sin θ < 0
5. 5.

   Esme works out cos 150° on a unit circle worksheet. The figure shades its reference angle, 30°. What is cos 150°?

   • -√3/2
   • 1/2
   • √3/2
   • -1/2
6. 6.

   Jun works out sin 225° on a unit circle worksheet. The figure shades its reference angle, 45°. What is sin 225°?

   • √2/2
   • -1/2
   • -√2/2
   • 1/2
7. 7.

   Luz's math book asks for cos 240°. The figure shades its reference angle, 60°. What is cos 240°?

   • -√3/2
   • -1/2
   • √3/2
   • 1/2

8. Read this first

   Use this

   csc θ = 1 ÷ sin θ, sec θ = 1 ÷ cos θ, cot θ = cos θ ÷ sin θ.

9. 8.

   On Milo's unit circle worksheet, a turn θ has sin θ = 3/5 and cos θ = -4/5. What is csc θ?

   5/3
10. 9.

    On Pia's unit circle worksheet, a turn θ has sin θ = -24/25 and cos θ = -7/25. What is csc θ?

    -25/24
11. 10.

    Ren's robot stops after a turn θ, where sin θ = 8/17 and cos θ = -15/17. What is sec θ?

    -17/15