Unit 7: Introduction to Trigonometry

Chapter Overview

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This unit introduces trigonometric ratios, their definitions in a right-angled triangle, and standard trigonometric values. Key concepts include sin, cos, tan, cosec, sec, cot, reciprocal relations, and basic identities. This unit is very important for FBISE board exams.

Multiple Choice Questions (MCQs)

Q1. Trigonometry is the branch of mathematics that deals with:

A. Circles
B. Triangles
C. Angles and sides of triangles
D. Polygons

Q2. In a right-angled triangle, sine of an acute angle is defined as:

A. Adjacent / Hypotenuse
B. Opposite / Hypotenuse
C. Opposite / Adjacent
D. Hypotenuse / Opposite

Q3. Cosine of an acute angle θ is:

A. Opposite / Hypotenuse
B. Adjacent / Hypotenuse
C. Opposite / Adjacent
D. Hypotenuse / Adjacent

Q4. Tangent of an acute angle θ is:

A. Adjacent / Opposite
B. Hypotenuse / Opposite
C. Opposite / Adjacent
D. Hypotenuse / Adjacent

Q5. Which of the following is the reciprocal of sin θ?

A. sec θ
B. cos θ
C. cosec θ
D. tan θ

Q6. The reciprocal of cos θ is:

A. tan θ
B. cot θ
C. sec θ
D. cosec θ

Q7. The reciprocal of tan θ is:

A. cot θ
B. sec θ
C. cos θ
D. sin θ

Q8. Which of the following is equal to sin θ / cos θ?

A. cot θ
B. sec θ
C. tan θ
D. cosec θ

Q9. In a right-angled triangle, the longest side is called:

A. Adjacent
B. Opposite
C. Hypotenuse
D. Base

Q10. The value of sin 0° is:

A. 1
B. 0
C. 1/2
D. √3/2

Q11. The value of cos 0° is:

A. 0
B. 1
C. √3/2
D. 1/2

Q12. The value of tan 0° is:

A. 1
B. √3
C. Undefined
D. 0

Q13. The value of sin 30° is:

A. 1
B. √3/2
C. 1/2
D. 0

Q14. The value of cos 60° is:

A. 1/2
B. √3/2
C. 1
D. 0

Q15. The value of tan 45° is:

A. 0
B. 1
C. √3
D. 1/√3

Q16. The value of sin 90° is:

A. 0
B. 1/2
C. √3/2
D. 1

Q17. The value of cos 90° is:

A. 0
B. 1
C. √3/2
D. 1/2

Q18. The value of tan 90° is:

A. 0
B. 1
C. √3
D. Not defined

Q19. Which trigonometric ratio is equal to 1/sin θ?

A. sec θ
B. cos θ
C. cosec θ
D. tan θ

Q20. Which trigonometric ratio is equal to 1/cos θ?

A. tan θ
B. cosec θ
C. cot θ
D. sec θ

Q21. If sin θ = 3/5, then cos θ is:

A. 4/5
B. 5/3
C. 3/4
D. 5/4

Q22. If tan θ = 1, then θ is:

A. 30°
B. 45°
C. 60°
D. 90°

Q23. Which of the following is always true?

A. sin θ = cos θ
B. sin²θ + cos²θ = 1
C. tan θ = 1
D. sec θ = cosec θ

Q24. Which angle is considered in basic trigonometry?

A. Obtuse angle
B. Acute angle
C. Reflex angle
D. Straight angle

Q25. In ΔABC right-angled at B, hypotenuse is:

A. AB
B. BC
C. AC
D. BA

Q26. The trigonometric ratio cosec θ is defined as:

A. Hypotenuse / Opposite
B. Adjacent / Hypotenuse
C. Opposite / Adjacent
D. Hypotenuse / Adjacent

Q27. The value of cos 30° is:

A. 1/2
B. √3/2
C. 1
D. 0

Q28. The value of tan 60° is:

A. 1
B. 1/√3
C. √3
D. 0

Q29. Which of the following ratios is undefined at 0°?

A. sin 0°
B. cos 0°
C. tan 0°
D. cosec 0°

Q30. If θ is an acute angle, then sin θ is always:

A. Negative
B. Zero
C. Positive
D. Undefined

Q31. The trigonometric ratios are defined only for:

A. Any triangle
B. Right-angled triangle
C. Isosceles triangle
D. Equilateral triangle

Q32. Which ratio is also called tangent?

A. sin θ / cos θ
B. cos θ / sin θ
C. 1 / sin θ
D. 1 / cos θ

Q33. The value of sec 60° is:

A. 2
B. 1/2
C. √3
D. √3/2

Q34. The value of cosec 30° is:

A. 1/2
B. √3/2
C. 2
D. √3

Q35. Which of the following is the correct identity?

A. sin θ = 1/cos θ
B. sec θ = 1/cos θ
C. tan θ = 1/sin θ
D. cot θ = 1/sec θ

Q36. The value of cot 45° is: