MCQ Mathematics Chapter 3: TRIGONOMETRIC FUNCTIONS, HS 1st year

 

1. The term "trigonometry" is derived from which of the following languages?
   a) Latin
   b) Greek
   c) Sanskrit
   d) Arabic
   Answer: b) Greek

2. One complete revolution of the initial side subtends an angle of how many radians?
   a) π
   b) 2π
   c) π/2
   d) 360
   Answer: b) 2π

3. What is the relationship between degrees and radians?
   a) 360° = π radians
   b) 180° = 2π radians
   c) 180° = π radians
   d) 90° = π/4 radians
   Answer: c) 180° = π radians

4. In the third quadrant, which trigonometric functions are positive?
   a) Sine and cosine
   b) Tangent and cotangent
   c) Sine and cosecant
   d) Cosine and secant
   Answer: b) Tangent and cotangent

5. What is the value of sin(0°)?
   a) 0
   b) 1
   c) -1
   d) Undefined
   Answer: a) 0

6. If cos x = -3/5 and x lies in the third quadrant, what is sin x?
   a) 4/5
   b) -4/5
   c) 3/5
   d) -3/5
   Answer: b) -4/5

7. What is the radian measure of an angle of 90°?
   a) π/3
   b) π/2
   c) π
   d) 2π
   Answer: b) π/2

8. Which of the following identities is correct?
   a) cos²x + sin²x = 2
   b) sin²x = 1 - cos²x
   c) 1 + cot²x = sec²x
   d) tan²x = 1 + sin²x
   Answer: b) sin²x = 1 - cos²x

9. If sin x = 3/5 and x lies in the second quadrant, what is cos x?
   a) 4/5
   b) -4/5
   c) 3/5
   d) -3/5
   Answer: b) -4/5

10. Which of the following is a periodic function with a period of 2π?
    a) tan x
    b) cot x
    c) sin x
    d) sec x
    Answer: c) sin x

11. The historical development of trigonometry is associated with which ancient mathematician?
    a) Aryabhatta
    b) Newton
    c) Pythagoras
    d) Euler
    Answer: a) Aryabhatta

12. What is the value of tan(45°)?
    a) 0
    b) 1
    c) √3
    d) Undefined
    Answer: b) 1

13. In which quadrant are both sine and cosine negative?
    a) First
    b) Second
    c) Third
    d) Fourth
    Answer: c) Third

14. The formula for converting radians to degrees is:
    a) Multiply radians by π/180
    b) Multiply radians by 180/π
    c) Divide radians by 180/π
    d) Divide radians by π/180
    Answer: b) Multiply radians by 180/π

15. What is the sine of an angle in the fourth quadrant?
    a) Always positive
    b) Always negative
    c) Undefined
    d) Equal to the cosine
    Answer: b) Always negative

16. Which trigonometric function is undefined for angles where cosine is 0?
    a) Tangent
    b) Cotangent
    c) Secant
    d) Cosecant
    Answer: c) Secant

17. What is the value of sin(30°)?
    a) √3/2
    b) 1/2
    c) 1
    d) 0
    Answer: b) 1/2

18. The value of cos(90°) is:
    a) 1
    b) -1
    c) 0
    d) Undefined
    Answer: c) 0

19. The formula for the arc length $l$ of a circle in terms of radius $r$ and angle $θ$ (in radians) is:
    a) $l = rθ$
    b) $l = θ/r$
    c) $l = θ^2/r$
    d) $l = r/θ$
    Answer: a) $l = rθ$

20. Which identity is correct for all x?
    a) $\tan^2x + 1 = \cot^2x$
    b) $\tan^2x + 1 = \sec^2x$
    c) $\sin^2x + \tan^2x = 1$
    d) $\cot^2x + 1 = \tan^2x$
    Answer: b) $\tan^2x + 1 = \sec^2x$

21. The value of $\cos(-x)$ is equal to:
    a) $-\cos x$
    b) $\cos x$
    c) $\sin x$
    d) $-\sin x$
    Answer: b) $\cos x$

22. What is the radian measure of an angle whose degree measure is 360°?
    a) $π/2$
    b) $π$
    c) $2π$
    d) $3π$
    Answer: c) $2π$

23. What is the value of $\tan(0°)$?
    a) 1
    b) Undefined
    c) 0
    d) Infinite
    Answer: c) 0

24. If $\sin x = 0$, then $x$ can be:
    a) $nπ$, where $n$ is any integer
    b) $(2n+1)π$, where $n$ is any integer
    c) $(nπ)/2$, where $n$ is any integer
    d) None of these
    Answer: a) $nπ$, where $n$ is any integer

25. The reciprocal of the sine function is:
    a) Secant
    b) Cosecant
    c) Tangent
    d) Cotangent
    Answer: b) Cosecant

26. The cosine of an angle in the second quadrant is always:
    a) Positive
    b) Negative
    c) Zero
    d) Undefined
    Answer: b) Negative

27. If $\tan x = 0$, $x$ must be equal to:
    a) $nπ$
    b) $(nπ)/2$
    c) $(2n+1)π/2$
    d) None of these
    Answer: a) $nπ$

28. In a right triangle, the ratio of opposite side to hypotenuse is called:
    a) Cosine
    b) Tangent
    c) Sine
    d) Secant
    Answer: c) Sine

29. The value of $\csc(90°)$ is:
    a) Undefined
    b) 0
    c) 1
    d) Infinity
    Answer: c) 1

30. The unit circle is a circle with radius equal to:
    a) 1 unit
    b) π units
    c) 2π units
    d) Infinite units
    Answer: a) 1 unit

31. The graph of $\sin x$ repeats after an interval of:
    a) $π$
    b) $2π$
    c) $π/2$
    d) None of these
    Answer: b) $2π$

32. The values of trigonometric functions for angles greater than 360° are:
    a) Undefined
    b) Periodic
    c) Same as their values for angles less than 360°
    d) Both b and c
    Answer: d) Both b and c

33. What is the reciprocal of $\cot x$?
    a) $\sin x$
    b) $\tan x$
    c) $\cos x$
    d) $\sec x$
    Answer: b) $\tan x$

34. The value of $\sin(180°)$ is:
    a) 1
    b) -1
    c) 0
    d) Undefined
    Answer: c) 0

35. What is the period of $\tan x$?
    a) $π$
    b) $2π$
    c) $π/2$
    d) Undefined
    Answer: a) $π$

36. The values of $\sin x$ range between:
    a) 0 to 1
    b) -1 to 1
    c) -∞ to ∞
    d) None of these
    Answer: b) -1 to 1

37. In the fourth quadrant, $\tan x$ is always:
    a) Positive
    b) Negative
    c) Undefined
    d) Zero
    Answer: b) Negative

38. If $\cos x = 0$, $x$ is equal to:
    a) $nπ$
    b) $(nπ)/2$, $n$ is odd
    c) $(nπ)/2$, $n$ is even
    d) None of these
    Answer: b) $(nπ)/2$, $n$ is odd

39. The value of $\sec(0°)$ is:
    a) 0
    b) 1
    c) Undefined
    d) Infinite
    Answer: b) 1

40. The coordinates of the point $P$ on the unit circle for an angle $π/2$ are:
    a) (0, 1)
    b) (1, 0)
    c) (-1, 0)
    d) (0, -1)
    Answer: a) (0, 1)

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More MCQs (41-75)

41. The value of $\sin^2x + \cos^2x$ is always:
    a) 2
    b) 1
    c) 0
    d) Undefined
    Answer: b) 1

42. The angle $π/6$ in degrees is:
    a) 30°
    b) 60°
    c) 90°
    d) 180°
    Answer: a) 30°

43. The tangent function is positive in which quadrants?
    a) I and III
    b) I and IV
    c) II and III
    d) II and IV
    Answer: a) I and III

44. What is the value of $\tan(π/4)$?
    a) 0
    b) 1
    c) Undefined
    d) √3
    Answer: b) 1

45. The angle $3π/2$ in degrees is:
    a) 270°
    b) 180°
    c) 90°
    d) 360°
    Answer: a) 270°

46. What is the value of $\cot(π/2)$?
    a) Undefined
    b) 0
    c) 1
    d) -1
    Answer: a) Undefined

47. If $\csc x = 2$, what is $\sin x$?
    a) 1/2
    b) -1/2
    c) 2
    d) Undefined
    Answer: a) 1/2

48. In a right triangle, which ratio represents $\tan x$?
    a) Adjacent / Hypotenuse
    b) Opposite / Adjacent
    c) Opposite / Hypotenuse
    d) Hypotenuse / Adjacent
    Answer: b) Opposite / Adjacent

49. The reciprocal of $\sec x$ is:
    a) $\sin x$
    b) $\cos x$
    c) $\tan x$
    d) $\cot x$
    Answer: b) $\cos x$

50. If $\tan x = 1$, $x$ could be:
    a) $π/2$
    b) $π/4$
    c) $π/3$
    d) $2π$
    Answer: b) $π/4$

76. If $\cos x = 0.6$ and $\sin x = 0.8$, then $\tan x$ is:
    a) $0.75$
    b) $1.33$
    c) $0.5$
    d) $1.5$
    Answer: b) $1.33$

77. Which of the following functions has a period of $π$?
    a) $\sin x$
    b) $\cos x$
    c) $\tan x$
    d) $\sec x$
    Answer: c) $\tan x$

78. The value of $\sec(90°)$ is:
    a) 0
    b) Undefined
    c) 1
    d) Infinite
    Answer: b) Undefined

79. The sum of squares of sine and cosine functions is:
    a) Always greater than 1
    b) Always less than 1
    c) Always equal to 1
    d) Undefined
    Answer: c) Always equal to 1

80. What is the value of $\cot(45°)$?
    a) 0
    b) 1
    c) Undefined
    d) $\sqrt{3}$
    Answer: b) 1

81. The range of the $\sin x$ function is:
    a) [0, 1]
    b) [-1, 1]
    c) (-∞, ∞)
    d) None of these
    Answer: b) [-1, 1]

82. What is the value of $\cos(\pi)$?
    a) -1
    b) 0
    c) 1
    d) Undefined
    Answer: a) -1

83. If $\tan x = 3/4$, $\sec x$ is:
    a) $5/4$
    b) $5/3$
    c) $4/3$
    d) $5/2$
    Answer: b) $5/3$

84. The reciprocal of $\csc x$ is:
    a) $\sin x$
    b) $\cos x$
    c) $\sec x$
    d) $\cot x$
    Answer: a) $\sin x$

85. In the second quadrant, which trigonometric functions are positive?
    a) $\sin x$ and $\cos x$
    b) $\sin x$ and $\csc x$
    c) $\tan x$ and $\sec x$
    d) $\cos x$ and $\sec x$
    Answer: b) $\sin x$ and $\csc x$

86. What is the value of $\tan(60°)$?
    a) $\sqrt{3}$
    b) $1/\sqrt{3}$
    c) $1$
    d) Undefined
    Answer: a) $\sqrt{3}$

87. The angle $\pi/3$ in degrees is:
    a) 30°
    b) 45°
    c) 60°
    d) 90°
    Answer: c) 60°

88. The cosine of an angle in the third quadrant is always:
    a) Positive
    b) Negative
    c) Zero
    d) Undefined
    Answer: b) Negative

89. What is the period of $\sec x$?
    a) $π$
    b) $2π$
    c) $π/2$
    d) $4π$
    Answer: b) $2π$

90. Which of the following is true for all $x$?
    a) $\csc x \cdot \sin x = 0$
    b) $\sec x \cdot \cos x = 1$
    c) $\tan x \cdot \cot x = 2$
    d) $\sin x \cdot \cos x = 1$
    Answer: b) $\sec x \cdot \cos x = 1$

91. The value of $\sin(-x)$ is:
    a) $\sin x$
    b) $-\sin x$
    c) $\cos x$
    d) $-\cos x$
    Answer: b) $-\sin x$

92. What is the radian measure of $120°$?
    a) $\pi/3$
    b) $2\pi/3$
    c) $3\pi/4$
    d) $4\pi/5$
    Answer: b) $2\pi/3$

93. If $\cos x = -0.5$ and $x$ lies in the third quadrant, what is $\sin x$?
    a) $\sqrt{3}/2$
    b) $-\sqrt{3}/2$
    c) $-1/2$
    d) Undefined
    Answer: b) $-\sqrt{3}/2$

94. The graph of $\cos x$ is symmetric about:
    a) $x = 0$
    b) $y = 0$
    c) $x = π$
    d) $x = π/2$
    Answer: a) $x = 0$

95. What is the slope of a line inclined at $45°$?
    a) 0
    b) 1
    c) $\sqrt{2}$
    d) Undefined
    Answer: b) 1

96. Which of the following angles lies in the fourth quadrant?
    a) $120°$
    b) $210°$
    c) $330°$
    d) $45°$
    Answer: c) $330°$

97. The function $\tan x$ is undefined at:
    a) $nπ$, where $n$ is an integer
    b) $(2n+1)π/2$, where $n$ is an integer
    c) $(nπ)/2$, where $n$ is an integer
    d) None of these
    Answer: b) $(2n+1)π/2$, where $n$ is an integer

98. If $\sin x = 0.6$, what is $\cos x$ assuming $x$ lies in the first quadrant?
    a) $0.8$
    b) $-0.8$
    c) $0.4$
    d) Undefined
    Answer: a) $0.8$

99. Which quadrant is $x = -45°$ located in?
    a) I
    b) II
    c) III
    d) IV
    Answer: d) IV

100. What is the value of $\tan(90°)$?
     a) 0
     b) 1
     c) Undefined
     d) Infinite
     Answer: c) Undefined

101. The maximum value of $\sin x$ is:
     a) 0
     b) -1
     c) 1
     d) Infinity
     Answer: c) 1

102. The minimum value of $\cos x$ is:
     a) -1
     b) 0
     c) 1
     d) Undefined
     Answer: a) -1

103. The general solution of $\sin x = 0$ is:
     a) $x = nπ$, $n \in Z$
     b) $x = (2n+1)π/2$, $n \in Z$
     c) $x = πn/2$, $n \in Z$
     d) None of these
     Answer: a) $x = nπ$, $n \in Z$

104. If $\csc x = -2$, then $x$ lies in which quadrant?
     a) I
     b) II
     c) III
     d) IV
     Answer: c) III

105. The formula $\cos(x+y) = \cos x \cos y - \sin x \sin y$ is called:
     a) Addition formula
     b) Subtraction formula
     c) Complementary angle formula
     d) Product-to-sum formula
     Answer: a) Addition formula

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