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Trigonometric functions Flashcards

1
Q

What is the sine of 90 degrees?

A

1

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2
Q

True or False: The cosine of 0 degrees is equal to 1.

A

True

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3
Q

Fill in the blank: The tangent function is defined as the ratio of ______ to ______.

A

sine to cosine

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4
Q

What is the value of sin(30 degrees)?

A

0.5

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5
Q

What is the range of the sine function?

A

-1 to 1

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6
Q

What is the period of the cosine function?

A

360 degrees or 2π radians

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7
Q

True or False: The tangent function is periodic with a period of 180 degrees.

A

True

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8
Q

What is the formula for the Pythagorean identity?

A

sin²(θ) + cos²(θ) = 1

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9
Q

What is the value of cos(180 degrees)?

A

-1

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10
Q

What is the cotangent function in terms of sine and cosine?

A

cot(θ) = cos(θ) / sin(θ)

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11
Q

What is the sine of 45 degrees?

A

√2 / 2

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12
Q

What is the cosine of 270 degrees?

A

0

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13
Q

Fill in the blank: The inverse of sine is called ______.

A

arcsine or sin⁻¹

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14
Q

What is the value of tan(90 degrees)?

A

undefined

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15
Q

What is the relationship between sine and cosine?

A

sin(θ) = cos(90° - θ)

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16
Q

True or False: The secant function is the reciprocal of the cosine function.

A

True

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17
Q

What is the value of sin(0 degrees)?

A

0

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18
Q

What is the derivative of sin(x)?

A

cos(x)

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19
Q

What is the value of tan(45 degrees)?

A

1

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20
Q

Fill in the blank: The cosecant function is the reciprocal of ______.

A

sine

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21
Q

What is the formula for converting degrees to radians?

A

radians = degrees × (π / 180)

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22
Q

What is the value of cos(90 degrees)?

A

0

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23
Q

What is the period of the sine function?

A

360 degrees or 2π radians

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24
Q

True or False: sin(θ) = sin(-θ).

A

False

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25
Q

What is the amplitude of a sine wave?

A

The maximum height of the wave, which is 1 for the standard sine function.

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26
Q

What is the value of tan(0 degrees)?

A

0

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27
Q

What is the range of the cosine function?

A

-1 to 1

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28
Q

What is the value of sec(0 degrees)?

A

1

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29
Q

Fill in the blank: The angle whose sine is 1 is ______ degrees.

A

90

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30
Q

What is the value of sin(360 degrees)?

31
Q

What is the cotangent of 45 degrees?

32
Q

What is the relationship between the cosecant and sine functions?

A

csc(θ) = 1/sin(θ)

33
Q

What is the formula for the double angle of sine?

A

sin(2θ) = 2sin(θ)cos(θ)

34
Q

What is the value of cos(60 degrees)?

35
Q

True or False: The sine function is an odd function.

36
Q

What is the value of tan(180 degrees)?

37
Q

What is the relationship between the sine and tangent functions?

A

tan(θ) = sin(θ) / cos(θ)

38
Q

Fill in the blank: The angle whose cosine is 0 is ______ degrees.

39
Q

What is the derivative of cos(x)?

40
Q

What is the value of csc(30 degrees)?

41
Q

What is the value of sec(60 degrees)?

42
Q

What is the value of sin(120 degrees)?

43
Q

True or False: The sine function has a maximum value of 2.

44
Q

What is the formula for the sum of angles for sine?

A

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

45
Q

What is the value of cot(0 degrees)?

46
Q

What is the relationship between the secant and cosine functions?

A

sec(θ) = 1/cos(θ)

47
Q

What is the value of sin(270 degrees)?

48
Q

Fill in the blank: The angle whose tangent is undefined is ______ degrees.

49
Q

What is the value of tan(60 degrees)?

50
Q

What is the value of csc(90 degrees)?

51
Q

What is the value of sec(45 degrees)?

52
Q

What is the formula for the cosine of the difference of two angles?

A

cos(a - b) = cos(a)cos(b) + sin(a)sin(b)

53
Q

What is the value of sin(150 degrees)?

54
Q

What is the value of cos(120 degrees)?

55
Q

True or False: The cosine function is an even function.

56
Q

What is the value of tan(30 degrees)?

57
Q

What is the value of cot(60 degrees)?

58
Q

What is the relationship between the cosecant and cotangent functions?

A

csc(θ) = 1/tan(θ) * cot(θ)

59
Q

What is the formula for the double angle of cosine?

A

cos(2θ) = cos²(θ) - sin²(θ)

60
Q

What is the value of csc(45 degrees)?

61
Q

What is the value of sec(30 degrees)?

62
Q

True or False: The sine of any angle is equal to the sine of its reference angle.

63
Q

What is the value of cos(45 degrees)?

64
Q

What is the value of tan(270 degrees)?

65
Q

What is the value of sin(240 degrees)?

66
Q

What is the value of cos(300 degrees)?

67
Q

What is the value of tan(120 degrees)?

68
Q

What is the value of csc(180 degrees)?

69
Q

What is the value of sec(90 degrees)?

70
Q

What is the angle whose tangent is 1?

A

45 degrees

71
Q

What is the value of cot(90 degrees)?

72
Q

What is the relationship between sine and the unit circle?

A

The sine of an angle corresponds to the y-coordinate of the point on the unit circle.

73
Q

What is the value of cos(0 degrees)?

Calculus (3 decks)

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