Question 1: Calculate the exact value of sin 45°.

Answer: √2 / 2

Question 2: Find cos 60° in simplest form.

Answer: 1/2

Question 3: What is the value of tan 30°?

Answer: 1/√3 or √3 / 3

Question 4: Construct a right triangle with a 45° angle, where the hypotenuse is 10 units. Label the lengths of the legs.

Answer: Legs are each 10/√2 units (or 5√2 units)

Question 5: Construct a triangle with a 30° angle, and hypotenuse 12 units. Calculate the lengths of the opposite and adjacent sides.

Answer: Opposite = 6, Adjacent = 6√3

Question 6: Plot the graph of y = 2x for x from 0 to 5 on the grid.

Answer: Line passing through points (0,0) to (5,10)

Question 7: Construct a triangle with sides 3, 4, and 5 units. Identify the angles with exact trig values for 30°, 45°, or 60° if applicable.

Answer: Right triangle with 90°, angles approx 36.87° and 53.13°, not matching 30°, 45°, 60° exactly

Question 8: A ladder leans against a wall forming a 60° angle with the ground. The ladder is 15 meters long. Find the height the ladder reaches on the wall.

Answer: Height = 15 * sin 60° = 15 * (√3/2) = 7.5√3 meters

Question 9: Explain why sin 45° equals cos 45°.

Answer: Because at 45°, the opposite and adjacent sides are equal in an isosceles right triangle, so sine and cosine are equal.

Question 10: Identify the common mistake made when students confuse sin and cos of 30°, and correct it.

Answer: Mistake: Using sin 30° = 1/2 and cos 30° = √3/2 interchangeably. Correction: Remember sin 30° = 1/2, cos 30° = √3/2.

Question 11: Challenge: Derive the exact value of sin 75° using sum identities.

Answer: sin 75° = sin(45° + 30°) = sin 45° * cos 30° + cos 45° * sin 30° = (√2/2)*(√3/2) + (√2/2)*(1/2) = (√6/4)+(√2/4) = (√6 + √2)/4