The sine of 30° is 1/2 and the cosine of 60° is also 1/2, so this Class 11 sheet opens with the two equal standard angles. The answers record 2π as the period of the sine and cosine functions, with 1 also recorded among later results.
Key Takeaways
sin 30° = 1/2 (Q1).
cos 60° = 1/2 (Q2).
Q6 records 2π as the period of the sine and cosine functions.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.The value of sin 30° is:
(a) 1/2(b) √3/2(c) 1/√2(d) 1
2.The value of cos 60° is:
(a) 1(b) 1/2(c) √3/2(d) 0
3.The value of sin 90° is:
(a) 0(b) 1/2(c) 1(d) √3/2
4.The value of tan 45° is:
(a) 0(b) 1(c) √3(d) Undefined
5.For any angle θ, sin² θ + cos² θ = ?
(a) 1(b) 0(c) tan² θ(d) 2
6.The period of the function y = sin x is:
(a) π(b) 2π(c) π/2(d) 3π
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.State the value of sin 150°.
8.Convert 45° into radians.
9.Find the value of cos 180°.
10.If tan θ = 3/4 and θ is acute, find sin θ.
11.State the identity relating 1 + tan² θ and sec² θ.
12.Find sin 75° using the formula for sin(A + B).
13.State the value of cos 120°.
14.Express sin 2A in terms of sin A and cos A.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.A vertical pole of height 20 m casts a shadow of length 20√3 m on the ground. Find the angle of elevation of the sun.
16.From the top of a tower 60 m high, the angle of depression of a car on the ground is 30°. Find the distance of the car from the foot of the tower.
17.A kite is flying at a height of 50 m. The string makes an angle of 30° with the horizontal. Find the length of the string.
18.The minute hand of a clock is 7 cm long. Find the area swept by the minute hand in 30 minutes.
19.A ladder leaning against a wall makes an angle of 60° with the ground and its foot is 2.5 m away from the wall. Find the length of the ladder.
20.An arc of length 5π cm subtends an angle at the centre of a circle of radius 10 cm. Find the angle subtended in radians.
Answer Key
1. a) 1/2
2. b) 1/2
3. c) 1
4. b) 1
5. a) 1
6. b) 2π
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
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14. Refer to solution guide.
15. Refer to solution guide.
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 the value of sin 30°?
1/2, option (a) in this worksheet (Q1).
What is the value of cos 60°?
1/2, option (b) in this worksheet (Q2).
What is the period of sin x?
2π, option (b) in this worksheet (Q6).
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