trigMultipleChoice.txt

1) What is the period of the function y = sin(x)?
   A) π
   B) x
   C) 2π
   D) 1
   Answer: C

2) What is the amplitude of y = 3cos(x)?
   A) 2π
   B) 3
   C) 1
   D) x
   Answer: B

3) sin²(x) + cos²(x) = ?
   A) π
   B) 2sin(x)
   C) undefined
   D) 1
   Answer: D

4) What is the value of tan(45°)?
   A) 1
   B) π
   C) 2π
   D) -π
   Answer: A

5) What is the reciprocal of sin(x)?
   A) tan(x)
   B) csc(x)
   C) sec(x)
   D) cot(x)
   Answer: B

6) What is the general form of the sine function?
   A) y = sin(Bx - C)
   B) y = A sin(Bx - C) + D
   C) y = sin(x)
   D) y = A sin(Bx - C)
   Answer: B

7) Which identity converts a product of sines into a sum?
   A) sin(A)sin(B) = [cos(A−B) + cos(A+B)]/2
   B) sin(A)sin(B) = [cos(A−B) − cos(A+B)]/2
   C) sin(A)sin(B) = 2[cos(A−B) − cos(A+B)]
   D) sin(A)sin(B) = [cos(A−B) − cos(A+B)]
   Answer: B

8) If y = 2sin(2x), what is its period?
   A) 2π
   B) π
   C) π/2
   D) 1
   Answer: A

9) What is the range of y = -2cos(x)?
   A) [0, 2π]
   B) [-2π, 0]
   C) [-2, 2]
   D) [-2π, 2π]
   Answer: C

10) What is the phase shift of y = sin(x - π/2)?
   A) 2π
   B) x
   C) π/2
   D) -π/2
   Answer: C

11) What is the domain of y = tan(x)?
   A) [-2π, 2π]
   B) All Real Numbers
   C) x ≠ π + nπ, n integer
   D) x ≠ π/2 + nπ, n integer
   Answer: D

12) tan²(x) + 1 = ?
   A) 2 cos(x) sin(x)
   B) cos(x) sin(x)
   C) sec(x)
   D) sec²(x)
   Answer: D

13) What is the reciprocal of tan(x)?
   A) cot(x)
   B) amplitude = 1
   C) 0
   D) sin(x)
   Answer: A

14) How do you find the amplitude of y = A sin(x)?
   A) range = [-1, 1]
   B) -1
   C) undefined
   D) The amplitude is |A|
   Answer: D

15) What is the period of y = sin(Bx)?
   A) csc(x)
   B) undefined
   C) 2π / B
   D) sec(x)
   Answer: C

16) What is sin(0°)?
   A) π/2
   B) 0
   C) -1
   D) π
   Answer: B

17) What is cos(90°)?
   A) 0
   B) π/2
   C) sec(x)
   D) π
   Answer: A

18) What is the value of sin(90°)?
   A) 2π
   B) All real numbers
   C) 1
   D) sec(x)
   Answer: C

19) What is the period of y = tan(x)?
   A) -1
   B) cos(x)
   C) π
   D) sin(x)
   Answer: C

20) What is the range of sin(x)?
   A) amplitude = 1
   B) [-1, 1]
   C) sec(x)
   D) 180°
   Answer: B

21) What is the unit circle?
   A) π
   B) Circle radius 1 at origin 
   C) All real numbers
   D) undefined
   Answer: B

22) What quadrant is sin(x) positive in?
   A) All real numbers
   B) Quadrants I and II
   C) π/2
   D) Period = π
   Answer: B

23) Which quadrant has all trig functions positive?
   A) 0
   B) π/3
   C) Period = π
   D) Quadrant I
   Answer: D

24) What is an even trig function?
   A) -1
   B) 2π
   C) cos(x) and sec(x)
   D) csc(x)
   Answer: C

25) What is an odd trig function?
   A) sec(x)
   B) [-1, 1]
   C) All real numbers
   D) sin(x), tan(x), csc(x), cot(x)
   Answer: D

26) What does 'co-function' mean?
   A) sin(θ) = cos(90° − θ)
   B) -1
   C) Period = π
   D) π
   Answer: A

27) Convert 180° to radians.
   A) csc(x)
   B) [-1, 1]
   C) π
   D) amplitude = 1
   Answer: C

28) Convert π/3 radians to degrees.
   A) 60°
   B) sin(x)
   C) Period = π
   D) cot(x)
   Answer: A

29) What is the graph of y = sin(x) like?
   A) 90°
   B) Wave oscillates between -1 and 1 every 2π
   C) csc(x)
   D) undefined
   Answer: B

30) What is the graph of y = tan(x) like?
   A) Curve with vertical asymptotes at odd multiples of π/2
   B) 2π
   C) [-1, 1]
   D) -1
   Answer: A

31) What identity is cos²(x) - sin²(x)?
   A) 90°
   B) 180°
   C) cos(2x)
   D) π/2
   Answer: C

32) What is sin(2x) equal to?
   A) 2 sin(x) cos(x)
   B) sec(x)
   C) amplitude = 1
   D) range = [-1, 1]
   Answer: A

33) What is cos(2x) equal to?
   A) π/2
   B) cos²(x) − sin²(x), or 2cos²(x)−1, or 1−2sin²(x)
   C) cos(x)
   D) 0
   Answer: B

34) How do you find a reference angle?
   A) 1
   B) Acute angle between terminal side and x-axis
   C) 2π
   D) cot(x)
   Answer: B

35) What is the cotangent of 0°?
   A) π/3
   B) cot(x)
   C) 90°
   D) Undefined
   Answer: D

36) What is sec(0°)?
   A) tan(x)
   B) cot(x)
   C) 1
   D) cos(x)
   Answer: C

37) What is csc(90°)?
   A) -1
   B) csc(x)
   C) 1
   D) π/3
   Answer: C

38) How do you identify vertical shift in a trig function?
   A) π/2
   B) cos(x)
   C) -1
   D) '+ D' at the end
   Answer: D

39) What does B affect in y = A sin(Bx)?
   A) -1
   B) π
   C) 2π
   D) Period
   Answer: D

40) What is the amplitude of y = -4sin(x)?
   A) 4 (negative reflects graph)
   B) sin(x)
   C) 0
   D) π
   Answer: A

41) If sin(x) = 1/2, what is x?
   A) π/3
   B) [-1, 1]
   C) 30° or 150°
   D) π
   Answer: C

42) What is arcsin(1)?
   A) cos(x)
   B) cot(x)
   C) 180°
   D) 90°
   Answer: D

43) What is arccos(0)?
   A) 2π
   B) 90°
   C) 1
   D) π
   Answer: B

44) What is arctan(1)?
   A) 180°
   B) π/3
   C) 45°
   D) 0
   Answer: C

45) How do you find the phase shift in y = sin(Bx − C)?
   A) 90°
   B) cos(x)
   C) C / B
   D) cot(x)
   Answer: C

46) What is the period of y = 5sin(3x)?
   A) csc(x)
   B) 2π / 3
   C) tan(x)
   D) π/2
   Answer: B

47) How do you find the maximum of y = A sin(x) + D?
   A) 1
   B) A + D
   C) 0
   D) [-1, 1]
   Answer: B

48) How do you find the minimum of y = A sin(x) + D?
   A) 90°
   B) 1
   C) [-1, 1]
   D) -A + D
   Answer: D

49) What does D represent in y = A sin(Bx) + D?
   A) 1
   B) π/2
   C) Vertical shift
   D) csc(x)
   Answer: C

50) How does a negative amplitude affect the graph?
   A) cot(x)
   B) Period = π
   C) [-1, 1]
   D) Reflects graph across x-axis
   Answer: D