11th grade Trig values by reference angle and quadrant sign, and the reciprocal ratios worksheet

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

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.

   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
3. 3.

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

   • -1/2
   • 1/2
   • -√3/2
   • √3/2
4. 4.

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

   • -√2/2
   • √2/2
   • 1/2
   • -1/2
5. 5.

   Kira's math book asks for sin 300°. The figure shades its reference angle, 60°. What is sin 300°?

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

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

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

7. Read this first

   Use this

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

8. 7.

   On Milo's unit circle worksheet, a turn θ has sin θ = 3/5 and cos θ = -4/5. What is csc θ?
9. 8.

   Noah's robot stops after a turn θ, where sin θ = -12/13 and cos θ = 5/13. What is sec θ?
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?
11. 10.

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