Question 1: Calculate the value of θ, where θ = sin⁻¹(0.5).

Answer: 30

Question 2: Evaluate cos⁻¹(0.8) to the nearest degree.

Answer: 36

Question 3: Find θ if tan⁻¹(1) = θ.

Answer: 45

Question 4: Plot on the grid the graph of y = sin⁻¹(x) for x in the range [-1, 1].

Answer: Student to draw the inverse sine curve.

Question 5: Construct a right-angled triangle with an angle of 30°, where the hypotenuse is 10 units. Use inverse functions to find the length of the side opposite the 30° angle.

Answer: 5 units

Question 6: Solve for θ: sin θ = 0.3, with 0° ≤ θ ≤ 180°.

Answer: 17.5

Question 7: A ladder leaning against a wall makes an angle of 60° with the ground. If the ladder is 12 meters long, use inverse functions to find the height it reaches on the wall.

Answer: 10.4 meters

Question 8: Given that cos⁻¹(0.6) is approximately 53.13°, identify and correct a common mistake: students think cos⁻¹(0.6) = 0.6°.

Answer: Cos⁻¹(0.6) gives an angle, not a value in degrees directly; students must use inverse cosine function, not interpret 0.6 as degrees.

Question 9: Calculate the angle θ where tan θ = 2. Use inverse tangent.

Answer: 63.4

Question 10: A person looks at the top of a building and measures the angle of elevation as 45°. If the person is 20 meters from the building, use inverse functions to find the height of the building (including the person's height, which is 1.5 meters).

Answer: 20 meters

Question 11: Express the inverse function of y = 3x + 4 for x in terms of y.

Answer: x = (y - 4)/3

Question 12: Challenge: Find θ such that sin θ = -0.5, where θ is in the range [0°, 360°].

Answer: 210 or 330