Question 1: Calculate the exact value of sin 30°.

Answer: 1/2

Question 2: Determine cos 45° and express your answer as a simplified fraction.

Answer: √2/2

Question 3: Find tan 60° by using exact trig values.

Answer: √3

Question 4: Construct a triangle with a 30° angle and hypotenuse of length 10 units. Label the side opposite the 30° angle.

Answer: 5 units

Question 5: Plot the graph of y = 2 sin x for x from 0° to 90° on your grid.

Answer: Curve passing through (30°, 1), (45°, √2), (60°, √3), (90°, 2)

Question 6: In a right-angled triangle where one angle is 45°, find the length of the side opposite this angle if the hypotenuse is 14 units.

Answer: 7√2

Question 7: A ladder leans against a wall, forming a 60° angle with the ground. If the ladder is 12 meters long, how high does it reach on the wall?

Answer: 6√3 meters

Question 8: Calculate the value of sin 45° and compare it to cos 45°. Are they equal? Explain briefly.

Answer: Yes, both are √2/2; they are equal because 45° angles in a right triangle are complementary.

Question 9: Identify and correct the mistake: "sin 60° = 1/2".

Answer: The correct value is √3/2, not 1/2.

Question 10: Using exact values, find the value of tan 30°.

Answer: 1/√3 or √3/3

Question 11: Estimate the value of sin 75° using known exact values and explain your reasoning.

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