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Pre-Calculus > Test 1 > Flashcards

Test 1 Flashcards

a. Know the Values of all functions(sin, cos, tan, csc, sec, cot) b. Know Reciprocal Identities c. Know Quotient Identities d. Know Pythagorean Identities e. Know Complementary/Cofunction Angles f. Know the exact values of 30, 45, and 60 degrees(for sin, cos, etc.) g. Know A. S. T. C.

1
Q

What is the value of Sine?

A

B/C or Opposite over Hypotenuse

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2
Q

What is the value of Cosine?

A

A/C or Adjacent over Hypotenuse

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3
Q

What is the value of Tangent?

A

B/A or Opposite over Adjacent

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4
Q

What is the value of Cosecant? What is it the reciprocal of?

A

C/B or Hypotenuse over Opposite. Is the reciprocal of Sine!

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5
Q

What is the value of Secant? What is it the reciprocal of?

A

C/A or Hypotenuse over Adjacent. Reciprocal of Cosine!

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6
Q

What is the value of Cotangent? What is it the reciprocal of?

A

A/B or Adjacent over Opposite. It’s the reciprocal of Tangent.

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7
Q

What is the Reciprocal Identity of Sine?

A

1/CSC or 1 over Cosecant

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8
Q

What is the Reciprocal Identity of Cosine?

A

1/SEC or 1 over Secant

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9
Q

What is the Reciprocal Identity of Tangent?

A

1/COT or 1 over Cotangent

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10
Q

What is the Reciprocal Identity of Cosecant?

A

1/SIN or 1 over Sine

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11
Q

What is the Reciprocal Identity of Secant?

A

1/COS or 1 over Cosine

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12
Q

What is the Reciprocal Identity of Cotangent?

A

1/TAN or 1 over Tangent

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13
Q

What is the Quotient Identity of Tangent?

A

SIN/COS or Sine over Cosine

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14
Q

What is the Quotient Identity of Cotangent?

A

COS/SIN or Cosine over Sine

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15
Q

What are the Pythagorean Identities?

A

a. Sin^2 + Cos^2 = 1
b. Tan^2 + 1 = Sec^2
c. Cot^2 + 1 = Csc^2

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16
Q

What is the Cofunction of Sin B?

A

Sin B = b/c = Cos A

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17
Q

What is the Cofunction of Cos B?

A

Cos B = a/c = Sin A

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18
Q

What is the Cofunction of Tan B?

A

Tan B = b/a = Cot A

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19
Q

What is the Cofunction of Csc B?

A

Csc B = c/b = Sec A

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20
Q

What is the Cofunction of Sec B?

A

Sec B = c/a = Csc A

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21
Q

What is the Cofunction of Cot B?

A

Cot B = a/b = Tan A

22
Q

What does A.S.T.C. mean?

A

All Students Take Calculus
A: All Positive
S: Sin/Csc positive
T: Tan/Cot, positive
C: Cos/Sec, positive

23
Q

What does adjacent turn into?

A

Adjacent -> X

24
Q

What does opposite turn into?

A

Opposite -> Y

25
Q

What does hypotenuse turn into?

A

Hypotenuse -> R

26
Q

What is the equation for R?

A

R = √x^2 + y^2

27
Q

For the Unit Circle what are the trigonometric values(formulas)?

A

R becomes 1 ( Hypotenuse becomes 1)
Sin = y
Cos = x
Tan = y/x
Csc = 1/y
Sec = 1/x
Cot = x/y

28
Q

What are the X & Y Intercepts of the graph y = Sin x?
(Domain, Range, Period, Amplitude, x & y intercepts)

A

X-intercepts: Kπ(occurs at every π value)
Y-intercepts: 0

29
Q

What are the Domain & Range of graph y = Sin x?

A

Odd Function
Domain; (-∞,∞)
Range: [-1,1]

30
Q

What are the Period & Amplitude of graph y = Sin x?

A

Period: 2π
Amp: 1

31
Q

What are the X & Y intercepts of the graph y = Cos x?

A

X-intercepts: π/2 + Kπ
Y-intercepts: 1

32
Q

What are the Domain & Range of the graph y = Cos x?

A

Even Function
Domain(-∞,∞)
Range: [-1,1]

33
Q

What are the Period & Amplitude of graph y = Cos x?

A

Period: 2π
Amp: 1

34
Q

What are the X & Y intercepts of the graph y = Tan x

A

X-intercepts: Kπ
Y-Intercepts: 0

35
Q

What are the Domain & Range of graph y = Tan x?

A

Odd Function
Domain: all real numbers except when x = π/2 + kπ
Range: (-∞,∞)

36
Q

What are the Period & Asymptotes of the graph y = Tan x?

A

Period: π
Asymptotes: x = π/2 + kπ

37
Q

What are the X & Y intercepts of the graph y = Cot x

A

X-Intercepts: π/2 + kπ
Y-intercepts: None

38
Q

What are the Domain & Range of the graph y = Cot x?

A

Odd Function
Domain: all real numbers except when x = kπ
Range: (-∞,∞)

39
Q

What are the Period & Asymptotes of the graph y = Cot x?

A

Period: π
Asymptotes: x = Kπ

40
Q

What are the X & Y intercepts of the graph y = Csc x?

A

X-Intercepts: None
Y-intercepts: None

41
Q

What are the Domain & Range of the graph y = Csc x?

A

Odd Function
Domain: all real numbers except when x = Kπ
Range: (-∞,-1] U [1,∞)

42
Q

What are the Period & Asymptotes of the graph y = Csc x?

A

Period: 2π
Asymptotes: x = Kπ

43
Q

What are the X & Y intercepts of the graph y = Sec x

A

X-Intercepts: None
Y-Intercepts: 1

44
Q

What are the Domain & Range of the graph y = Csc x?

A

Even Function
Domain: all numbers except when x = π/2 + kπ
Range: (-∞,-1] U [1,∞)

45
Q

What are the Period & Asymptotes of the graph y = Csc x?

A

Period: 2π
Asymptotes: X = π/2 + Kπ

46
Q

What does it mean for a function to be Odd?

A

A: The graph is symmetric to the origin( if you turn it upside-down, its the same graph you started with )
B: Sin (-x) = -Sin (x)

47
Q

What does it mean for a function to be Even?

A

A: The graph is symmetric to the y-axis ( if you you fold it across the y-axis, the graph lays on top of the other half of the graph
B: Cos (-x) = Cos (x)

48
Q

What do these functions mean:
f(x + h) & f(x - h)?

A

Transformation: Horizontal Shift-
A: f(x + h): Shift left h units
B: f(x - h): Shift right h units

49
Q

What do these functions mean:
f(x) + k & f(x) - k?

A

Transformation: Vertical Shift-
A: f(x) + k: Shift up k units
B: f(x) - k: Shift down k units

50
Q

What do these functions mean:
-f(x) & f(-x)?

A

Transformation: Reflection-
A: -f(x): Reflect across x-axis
B: f(-x): Reflect across y-axis

51
Q

What do these functions mean:
a f(x), a > 1 & a f(x), 0 < a < 1 ?

A

Transformation: Vertical Stretch/Compress-
a f(x), a > 1: Stretch vertically by a factor of a
a f(x), 0 < a < 1: Compress vertically by a factor of a

52
Q

What do these functions mean:
f(ax), a > 1 & f(ax), 0 < a < 1 ?

A

Transformation: Horizontal Stretch/Compress-
f(ax), a > 1: Compress horizontally by a factor of 1/a
f(ax), 0 < a < 1: Stretch horizontally by a factor of 1/a

Pre-Calculus (1 decks)

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