Inverse trig functions, and solving trigonometric equations

Answer Key - Grade 11 Math Worksheet

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

1. 1.

   Luz works out sin⁻¹(-1/2) on a unit circle worksheet. What is sin⁻¹(-1/2), in radians?

   • -30°
   • 2π/3
   • -π/6
   • 11π/6
2. 2.

   Milo's math book asks for cos⁻¹(-√3/2). What is cos⁻¹(-√3/2), in radians?

   • 5π/6
   • -π/3
   • 150°
   • 7π/6
3. 3.

   Noah works out tan⁻¹(√3) on a unit circle worksheet. What is tan⁻¹(√3), in radians?

   • -π/3
   • 4π/3
   • 60°
   • π/3
4. 4.

   Ren solves √2 sin x + 1 = 0 for 0° ≤ x < 360° on a worksheet, writing answers like 10, 20. What are all the solutions?

   225, 315
5. 5.

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

   45, 315
6. 6.

   Zee solves √3 tan x + 1 = 0 for 0° ≤ x < 360° on a worksheet, writing answers like 10, 20. What are all the solutions?

   150, 330
7. 7.

   Jun solves cos x = 1/2 for 0 ≤ x < 2π on a unit circle worksheet. Which list gives every solution?

   • π/3, 4π/3
   • π/3, 5π/3
   • π/3, 2π/3
   • π/3
8. 8.

   Kira's math book asks for every x with sin x = -1/2 and 0 ≤ x < 2π. Which list gives every solution?

   • 7π/6, 11π/6
   • 7π/6
   • -π/6, 7π/6
   • 5π/6, 7π/6
9. 9.

   Luz solves tan x = -1 for 0 ≤ x < 2π on a unit circle worksheet. Which list gives every solution?

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

    Milo's math book asks for every x with cos x = -√3/2 and 0 ≤ x < 2π. Which list gives every solution?

    • π/6, 11π/6
    • π/6, 5π/6
    • 5π/6
    • 5π/6, 7π/6