Cosine of 60° is 1/2, matching sine of 30° which is also 1/2, so this IB Year 12 sheet opens by comparing the two standard angles side by side. A ratio of 3/5 appears among the later answers of the worksheet.
Key Takeaways
cos 60° = 1/2 (Q2).
sin 30° = 1/2 (Q1).
Q5 records 3/5 among the trigonometric answers.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.What is sin 30°?
(a) 1/2(b) √3/2(c) 1(d) √2/2
2.What is cos 60°?
(a) √3/2(b) 1/2(c) 0(d) 1
3.What is tan 45°?
(a) √2(b) 0(c) 1(d) √3/2
4.What is sin(π/2)?
(a) 0(b) 1/2(c) √3/2(d) 1
5.In a right triangle the opposite side is 3 and the hypotenuse is 5. What is sin θ?
(a) 4/5(b) 3/5(c) 5/4(d) 3/4
6.What is cos(π/3)?
(a) √3/2(b) 1(c) 1/2(d) 0
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Evaluate sin² 30° + cos² 30°.
8.Solve sin x = 1 for 0 ≤ x ≤ 360°.
9.Simplify tan θ × cos θ.
10.In a right triangle the angle is 40° and the adjacent side is 10. Find the opposite side to 2 decimal places.
11.Convert 90° to radians.
12.In triangle ABC, angle A = 50°, angle B = 70° and a = 10. Use the sine rule to find b to 2 decimal places.
13.State the value of cos 0°.
14.State the amplitude of y = 3 sin x.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.A tree casts a shadow 12 m long when the sun's elevation is 35°. Find the height of the tree to 1 decimal place.
16.Find the area of a triangle with two sides 7 and 9 and an included angle of 40°. Give the answer to 1 decimal place.
17.Two sides of a triangle are 5 and 7 with an included angle of 60°. Use the cosine rule to find the third side to 2 decimal places.
18.From a point, the angle of elevation of the top of a tower is 30°. After moving 50 m closer, the angle is 45°. Find the tower's height to 1 decimal place.
19.A Ferris wheel seat is at height h(t) = 20 + 15 sin(2πt ÷ 30) metres. Find the maximum height of the seat.
20.Find the area of a sector with radius 6 cm and angle 60°. Give the answer in terms of π.
Answer Key
1. a) 1/2
2. b) 1/2
3. c) 1
4. d) 1
5. b) 3/5
6. c) 1/2
7. Refer to solution guide.
8. Refer to solution guide.
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10. Refer to solution guide.
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16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
What is sin 30°?
1/2, option (a) in this worksheet (Q1).
What is cos 60°?
1/2, option (b) in this worksheet (Q2).
What trigonometric value appears among the answers?
3/5, option (b) in this worksheet (Q5).
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