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Precalc > Trig > Flashcards

Trig Flashcards

1
Q

the x-coordinate of the point t
on the number circle.

A

cos t

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2
Q

the y-coordinate of the point t
on the number circle.

A

sin t

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3
Q

Period of Cosine

A

2pi

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4
Q

Period of Sine

A

2pi

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5
Q

cis(t) =

A

cos(t) + isin(t)

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6
Q

Is Cosine an even or odd function

A

Even

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7
Q

Formula for coterminal angles of cos

A

cos(t + 2kpi)

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8
Q

Is Sine an even or odd function

A

Odd

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9
Q

Formula for coterminal angles of sin

A

Sin(t + 2kpi)

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10
Q

Equation of the Unit Circle

A

x^2 + y^2 = 1

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11
Q

projection of t through the origin to the s-axis.

Also the slope of the line through the origin and t

A

tan t

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12
Q

projection of t through the origin to the r-axis.

Also the reciprocal slope of the line through the origin and t

A

cot t

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13
Q

What is the period of tan

A

pi

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14
Q

is tangent an even or odd function

A

odd

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15
Q

cos co-function identity

A

sin(pi/2 - t)

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16
Q

sin co-function identity

A

cos(pi/2 - t)

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17
Q

tan co-function identity

A

cot(pi/2 - t)

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18
Q

cot co-function identity

A

tan(pi/2 - t)

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19
Q

Is secant an even or odd function

A

even

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20
Q

Is Cosecant an even or odd function

A

odd

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21
Q

what are the periods of sec and csc

A

2kpi

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22
Q

reciprocal identity of csc(t)

A

1/sin(t)

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23
Q

reciprocal identity of sec(t)

A

1/cos(t)

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24
Q

reciprocal identity of cot(t)

A

1/tan(t)

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25
Q

reciprocal identity of sin(t)

A

1/csc(t)

26
Q

reciprocal identity of cos(t)

A

1/sec(t)

27
Q

reciprocal identity of tan(t)

A

1/cot(t)

28
Q

quotient identity of tan(t)

A

sin(t)/cos(t)

29
Q

tangent is positive in which quadrants

A

1 and 3

30
Q

sine is positive in which quadrants

A

1 and 2

31
Q

cosine is positive in which quadrants

A

1 and 4

32
Q

amplitude for sine and cosine

A

distance between top and bottom of wave divided by 2

33
Q

phase shift for sine and cosine

A

location of the peak closest to the x axis

34
Q

baseline

A

the mid-point of the wave

35
Q

formula for the period of sine and cosine

A

2pi / omega (ω)

36
Q

formula for phase shift

A
  • phi (φ) / omega (ω)
37
Q

What is the amplitude of the following:

3 sin (4t + pi/3) + 5

A

3

38
Q

What is the baseline of the following:

3 sin (4t + pi/3) + 5

A

5

39
Q

What is the phase of the following:

3 sin (4t + pi/3) + 5

A

pi/3

40
Q

What is the period of the following:

3 sin (4t + pi/3) + 5

A

2pi/4

41
Q

What is the phase shift of the following:

3 sin (4t + pi/3) + 5

A
  • (pi/3) / 4
42
Q

What is the formula for the period of Tangent

A

pi / omega (ω)

43
Q

How do you find the amplitude of Tangent

A

period / 4

44
Q

How do you find the asymptote of Tangent

A

period / 2

45
Q

Transformations formula for cosine

A

f(t) = a cos (ωt + φ) + b

46
Q

Where is the phase shift of Cotangent

A

The Asymptote

47
Q

How do you find the amplitude of Cotangent

A

period / 4

48
Q

Where is the period of cotangent

A

From asymptote to asymptote

49
Q

formula to find Tangent

A

y/x or sin/cos

50
Q

formula to find Cotangent

A

x/y or cos/sin

51
Q

cosine addition formula

A

cos(s + t) = cos(s) * cos(t) - sin(s) * sin(t)

52
Q

sine addition formula

A

sin(s + t) = cos(s) * sin(t) + sin(s) * cos(t)

53
Q

tangent addition formula (without simplification)

A

tan(s + t) = sin(s + t) / cos(s + t)

54
Q

tangent addition formula (simplified)

A

tan(t) + tan(s) / 1 - tan(t) * tan(s)

55
Q

cosine subtraction formula

A

cos(s - t) = cos(s) * cos(t) + sin(s) * sin(t)

56
Q

sine subtraction formula

A

sin(s - t) = sin(s) * cos(t) − cos(s) * sin(t)

57
Q

cosine double-angle formula

A

cos(2t) = cos^2(t) - sin^2(t)

58
Q

sine double-angle formula

A

sin(2t) = 2cos(t)sin(t)

59
Q

tangent subtraction formula

A

tan(α−β)= tan(α)−tan(β) / 1+tan(α)tan(β)

60
Q

tangent double-angle formula

A

tan(2t) = 2tan(t) / 1 - tan^2(t)

Precalc (1 decks)

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