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SAT & subject tests > math 2: trigonometric functions > Flashcards

math 2: trigonometric functions Flashcards

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SAT® Prep flashcards
1
Q

P(x, y) is any point on the

A

terminal side of the angel

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2
Q

r is the distance between

A

O and P

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3
Q

sinx =

A

y/r

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4
Q

cosx=

A

x/r

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5
Q

tanx=

A

y/x

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6
Q

cotx=

A

x/y

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7
Q

secx=

A

r/x

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8
Q

cscx=

A

r/y

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9
Q

sinx · cscx =

A

1

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10
Q

cosx · secx =

A

1

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11
Q

tanx · cotx =

A

1

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12
Q

tanx = sinx/

A

cosx

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13
Q

cotx= cosx/

A

sinx

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14
Q

cos²θ + sin²θ =

A

1

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15
Q

sin²θ =

A

1- cos²θ

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16
Q

cos²θ =

A

1-sin²θ

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17
Q

sec²θ =

A

1 + tan²θ

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18
Q

csc²θ =

A

cot²θ + 1

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19
Q

All Students

A

Take Calculus

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20
Q

angles of Q. II, IIII, or IV have

A

reference angles θr

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21
Q

any trig function of θ =

A

± the same function of θr (sign determined by quadrant)

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22
Q

sin & cos, tan & cot, sec & csc are

A

cofunction pairs

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23
Q

confuctions of complementary angles are

A

equal

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24
Q

if a and b are complementary, then

A

triga=cotrig(b) & trigb=cotrig(a)

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25
Q

one radian is about

A

57.3 degrees

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26
Q

length of an arc, s, is:

A

rθ

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27
Q

area of sector AOB is

A

1/2r²θ

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28
Q

domain of sine:

A

(-∞, +∞)

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29
Q

range of sine:

A

-1≤ sinx ≤1

30
Q

domain of cosine:

A

(-∞, +∞)

31
Q

range of cosine:

A

-1≤ cosx ≤1

32
Q

domain of tan:

A

{x| x≠ π/2 + πn, where n is an integer}

33
Q

range of tangent:

A

all real numbers

34
Q

domain of cot:

A

{x| x≠ πn, where n is an integer}`

35
Q

range of cotangent:

A

all real numbers

36
Q

domain of secant:

A

{x| x≠ π/2 + πn, where n is an integer}

37
Q

range of secant:

A

(-∞, -1] ∪ [1, +∞)

38
Q

domain of csc:

A

{x| x≠ πn, where n is an integer}

39
Q

range of csc:

A

(-∞, -1] ∪ [1, +∞)

40
Q

general form of a trig function: y=

A

A · trig(Bx + C) + D

41
Q

amplitude→

A

|A|

42
Q

horizontal translation (phase shift) →

A

-C/B

43
Q

horizontal dilation (period)

A

either 2π/B or π/B

44
Q

vertical translation→

A

D

45
Q

(reciprocal identities) cscx =

A

1/sinx

46
Q

(reciprocal identities) secx=

A

1/cosx

47
Q

(reciprocal identities) cotx=

A

1/tanx

48
Q

(cofunction identities) sinx=

A

cos(π/2 - x)

49
Q

(cofunction identities) secx=

A

csc(π/2 - x)

50
Q

(cofunction identities) tanx=

A

cot(π/2 - x)

51
Q

(cofunction identities) cosx=

A

sin(π/2 - x)

52
Q

(cofunction identities) cscx=

A

sec(π/2 - x)

53
Q

(cofunction identities) cotx=

A

tan(π/2 - x)

54
Q

(double angle identities) sin2x=

A

2(sinx)(cosx)

55
Q

(double angle identities) cos2x (both sin and cos)

A

= cos²x - sin²x

56
Q

(double angle identities) cos2x (just cos)

A

= 2cos²x - 1

57
Q

(double angle identities) cos2x (just sin)

A

= 1 - 2sin²x

58
Q

graphs of the inverses of trig functions aren’t graphs of functions, so the domain neeeds to be limited to one period for

A

range values to be achieved exactly once

59
Q

sin^-1 domain

A

[-1, 1]

60
Q

sin^-1 range

A

[-π/2, π/2]

61
Q

cos^-1 domain

A

[-1, 1]

62
Q

cos^-1 range

A

[0, π]

63
Q

tan^-1 domain

A

(-∞, +∞)

64
Q

tan^-1 range

A

(-π/2, π/2)

65
Q

cot^-1 domain

A

(-∞, +∞)

66
Q

cot^-1 range

A

(0, π)

67
Q

sec^-1 domain

A

(-∞, -1] ∪ [1, +∞)

68
Q

sec^-1 range

A

[0, π/2) ∪ (π/2, π]

69
Q

csc^-1 domain

A

(-∞, -1] ∪ [1, +∞)

70
Q

csc^-1 range

A

[-π/2, 0) ∪ (0, π/2]

SAT & subject tests (30 decks)

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