Question 1: Calculate the angle in degrees: if sin θ = 0.5, find θ using the inverse sine function.

Answer: 30

Question 2: Determine the angle in degrees: cos θ = 0.866, using the inverse cosine function.

Answer: 30

Question 3: Find θ in degrees: tan θ = 1, using the inverse tangent function.

Answer: 45

Question 1: A ladder leans against a wall forming an angle of 60° with the ground. The ladder's length is 10 meters. Use inverse functions to find the height the ladder reaches on the wall.

Answer: 5

Question 2: If sin θ = 0.6, explain why θ is not 36.87° but rather 36.87° or 143.13°, and determine the correct principal value of θ.

Answer: Principal value is 36.87°, because inverse sine returns values between -90° and 90°.

Question 1: A person is standing 50 meters from a tower. The angle of elevation to the top of the tower is 35°. Use inverse functions to find the height of the tower.

Answer: 37.4

Question 1: A triangle has an angle θ with sin θ = 0.8. Find all possible solutions for θ between 0° and 360°.

Answer: 36.87°, 143.13°

Question 2: Construct a triangle on the grid where the angle θ satisfies sin θ = 0.7. Mark the angle and sides.

Answer: Students draw and label accordingly.

Question 1: A student states that inverse sine of 1 equals 90°. Is this correct? If not, explain the mistake and give the correct answer.

Answer: No, inverse sine of 1 is 90°, but it is only valid in degrees; the value is correct, but students must understand the range of inverse functions.

Question 2: Identify the error: using inverse cosine gives the same result as inverse sine for the same ratio. Explain why this is incorrect and correct the reasoning.

Answer: Because sine and cosine functions have different ranges and there are multiple angles with the same ratio, students must consider the domain and range of inverse functions.