Question 1: Calculate the angle in degrees, θ, such that sin(θ) = 0.6.

Answer: 36.87

Question 2: Find the value of θ (in degrees) where cos(θ) = 0.8, using inverse cosine.

Answer: 36.87

Question 3: Determine θ in degrees if tan(θ) = 1.5.

Answer: 56.31

Question 4: Construct a triangle where one angle is 30°, and the sine of another angle is 0.5. Show the approximate value of that angle in degrees.

Answer: 30

Question 5: If sin(α) = 0.75, find α in degrees using inverse sine. Round to two decimal places.

Answer: 48.59

Question 6: A ladder leans against a wall making an angle of 60°. If the length of the ladder is 10 meters, find the height it reaches on the wall, using inverse functions.

Answer: 8.66

Question 7: Calculate the inverse cosine of 0.3 to find the angle in degrees.

Answer: 72.54

Question 8: A car turns at a radius of 50 meters making an angle of 45° with the radius. Find the angle of the car’s velocity vector relative to the radius using inverse tangent.

Answer: 45

Question 9: A surveyor measures a slope where tan(θ) = 2. The surveyor needs to find θ in degrees. Calculate this using inverse tangent.

Answer: 63.43

Question 10: Identify and correct the mistake: A student states that sin⁻¹(1) = 90°. Is this correct? Explain your reasoning.

Answer: Yes, because sin(90°) = 1.

Question 11: A cyclist looks at a tower and finds that the angle of elevation is 75°. If the height of the tower is 120 meters, what is the horizontal distance from the cyclist to the tower? Use inverse tangent.

Answer: 390.59