Question 1: Evaluate A = B^{-1} (0.5) where B(x) = \, ext{sin}^{-1}(x).

Answer: 30

Question 2: Find the angle C (in degrees) if A = B^{-1}(0.75) and B(x) = \, ext{cos}^{-1}(x).

Answer: 41

Question 3: Calculate A = C^{-1} (0.6) where C(x) = \, ext{tan}^{-1}(x).

Answer: 30.96

Question 4: Construct a triangle where A = B^{-1}(0.8) using the grid. State the approximate angle in degrees.

Answer: 36

Question 5: A ladder leans against a wall forming an angle A with the ground. The ladder's length is 10 meters, and A = B^{-1}(0.5). Find the height the ladder reaches on the wall.

Answer: 8.66

Question 6: Evaluate A = A^{-1}(1) where A(x) = \, ext{sin}(x).

Answer: 90

Question 7: Solve for x: A = B^{-1}(x) where B(x) = \, ext{cos}^{-1}(x) and A = 60b0.

Answer: 0.5

Question 8: Given A = B^{-1}(x) with B(x) = \, ext{tan}^{-1}(x), find x when A = 45b0.

Answer: 1

Question 9: Identify and correct the mistake: A = B^{-1}(x), where B(x) = \, ext{sin}(x). If students compute A = \, ext{sin}^{-1}(x) for x=1, they should get 90b0, but they write 180b0. What is the mistake?

Answer: Confusing sin^{-1} with sin; correct angle is 90b0, not 180b0.

Question 10: Challenge: If A = A^{-1}(x), find x such that A = 0.5 when A(x) = \, ext{cot}^{-1}(x).

Answer: 1