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Unit 2

This document contains model questions for a mathematics course on trigonometry, structured into three sections: short answer, medium answer, and long answer questions. It covers fundamental concepts such as radians, trigonometric functions, and various identities and formulas. The questions are based on exam patterns from the last ten years, focusing on proving and deriving key trigonometric identities and values.

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Dipankar Dey
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20 views1 page

Unit 2

This document contains model questions for a mathematics course on trigonometry, structured into three sections: short answer, medium answer, and long answer questions. It covers fundamental concepts such as radians, trigonometric functions, and various identities and formulas. The questions are based on exam patterns from the last ten years, focusing on proving and deriving key trigonometric identities and values.

Uploaded by

Dipankar Dey
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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Mathematics for Computing (GE3B-04)

Unit 2: Trigonometry - Model Questions


(Based on Last 10 Years of Exam Patterns)

Section A: Short Answer Questions (2 Marks Each)

1. Define radian and degree measure.


2. Convert 60° into radians.
3. Define trigonometric functions with examples.
4. Find the value of sin 45° and cos 30°.
5. State and prove sin²θ + cos²θ = 1.
6. Find the value of tan 90°.
7. What are allied angles? Give an example.
8. Define compound angles and give one example.
9. Find the sine and cosine of 180° + θ.
10. State and prove the formula for sin(A + B).

Section B: Medium Answer Questions (5 Marks Each)

11. Prove that cos(A + B) = cos A cos B – sin A sin B.


12. Show that tan(A + B) = (tan A + tan B) / (1 – tan A tan B).
13. Find sin 75° using the compound angle formula.
14. Derive the formulas for multiple angles.
15. Express sin 3θ and cos 3θ in terms of sinθ and cosθ.
16. Prove that sin 2θ = 2 sinθ cosθ.
17. If sin A = 3/5, find the value of cos A and tan A.
18. Find the values of trigonometric functions for θ = 225°.
19. Prove that cot(A + B) = (cot A cot B – 1) / (cot B + cot A).
20. Find sin 15° using trigonometric identities.

Section C: Long Answer Questions (10 Marks Each)

21. Prove that cos 2θ = cos²θ – sin²θ and derive its alternative forms.
22. Derive the formula for sin(A – B) and cos(A – B).
23. Prove that sec²θ – tan²θ = 1 using trigonometric identities.
24. Derive and prove the formulas for half-angle identities.
25. Prove that tan(45° + θ) = (1 + tanθ) / (1 – tanθ).
26. Show that sin 5θ = 5 sinθ – 20 sin³θ + 16 sin⁵θ.
27. Prove that sin²(A/2) = (1 – cos A) / 2.
28. Derive expressions for sin(A + B + C) in terms of individual sine and cosine values.
29. Solve the equation 2 sin x cos x = 1 for 0 ≤ x ≤ 360°.
30. If tan A = 4/3 and tan B = 3/4, find the value of tan(A + B).

End of Document

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