Inverse trig functions, and solving trigonometric equations

Answer Key - Grade 11 Math Worksheet - Building Confidence

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

1. 1.

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

   30
2. 2.

   Kira's math book asks for cos⁻¹(-1/2). What is cos⁻¹(-1/2), in degrees?

   120
3. 3.

   Luz works out sin⁻¹(-√3/2) on a unit circle worksheet. What is sin⁻¹(-√3/2), in degrees?

   -60
4. 4.

   Milo's math book asks for tan⁻¹(-√3). What is tan⁻¹(-√3), in degrees?

   -60
5. 5.

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

   30, 150
6. 6.

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

   120, 240
7. 7.

   Ren solves sin x = -√3/2 for 0° ≤ x < 360° on a worksheet, writing answers like 10, 20. What are all the solutions?

   240, 300
8. 8.

   it meets the circle at two points, mirror images across the x-axis. Tala's math book asks for every x with cos x = √3/2 and 0° ≤ x < 360°, written like 10, 20. What are the solutions?

   30, 330
9. 9.

   Esme's math book shows 2 cos x + 3 = 4. The first steps get cos x alone. What does cos x equal?

   1/2
10. 10.

    Jun starts solving 3 tan x + 5 = 2 on a worksheet by getting tan x alone. What does tan x equal?

    -1