Inverse trig functions, and solving trigonometric equations

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   Noah solves 4 sin²x = 3 for 0° ≤ x < 360° on a worksheet, writing answers like 10, 20. What are all the solutions?

   60, 120, 240, 300
2. 2.

   Pia's math book asks for every x with 2 cos²x = 1 and 0° ≤ x < 360°, written like 10, 20. What are the solutions?

   45, 135, 225, 315
3. 3.

   Ren solves 4 cos²x = 3 for 0° ≤ x < 360° on a worksheet, writing answers like 10, 20. What are all the solutions?

   30, 150, 210, 330
4. 4.

   Tala's math book asks for every x with 3 tan²x = 9 and 0° ≤ x < 360°, written like 10, 20. What are the solutions?

   60, 120, 240, 300
5. 5.

   Zee solves 2 sin²x − sin x = 0 for 0° ≤ x < 360° on a worksheet, writing answers like 10, 20. What are all the solutions?

   0, 30, 150, 180
6. 6.

   Esme's math book asks for every x with 2 cos²x + cos x = 0 and 0° ≤ x < 360°, written like 10, 20. What are the solutions?

   90, 120, 240, 270
7. 7.

   Kira's math book asks for every x with (2 cos x + √3)(sin x + 1) = 0 and 0° ≤ x < 360°, written like 10, 20. What are the solutions?

   150, 210, 270
8. 8.

   Luz solves 2 sin x + √3 = 0 for 0 ≤ x < 2π on a unit circle worksheet. Which list gives every solution?

   • 4π/3
   • -π/3, 4π/3
   • 4π/3, 5π/3
   • 2π/3, 4π/3
9. 9.

   Milo's math book asks for every x with √2 cos x + 1 = 0 and 0 ≤ x < 2π. Which list gives every solution?

   • 3π/4, 5π/4
   • 3π/4
   • π/4, 3π/4
   • π/4, 7π/4
10. 10.

    Noah solves tan x + √3 = 0 for 0 ≤ x < 2π on a unit circle worksheet. Which list gives every solution?

    • 2π/3
    • π/3, 2π/3
    • -π/3, 2π/3
    • 2π/3, 5π/3