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
What does hypotenuse turn into?
Hypotenuse -> R
26
What is the equation for R?
R = √x^2 + y^2
27
For the Unit Circle what are the trigonometric values(formulas)?
R becomes 1 ( Hypotenuse becomes 1) Sin = y Cos = x Tan = y/x Csc = 1/y Sec = 1/x Cot = x/y
28
What are the X & Y Intercepts of the graph y = Sin x? (Domain, Range, Period, Amplitude, x & y intercepts)
X-intercepts: Kπ(occurs at every π value) Y-intercepts: 0
29
What are the Domain & Range of graph y = Sin x?
Odd Function Domain; (-∞,∞) Range: [-1,1]
30
What are the Period & Amplitude of graph y = Sin x?
Period: 2π Amp: 1
31
What are the X & Y intercepts of the graph y = Cos x?
X-intercepts: π/2 + Kπ Y-intercepts: 1
32
What are the Domain & Range of the graph y = Cos x?
Even Function Domain(-∞,∞) Range: [-1,1]
33
What are the Period & Amplitude of graph y = Cos x?
Period: 2π Amp: 1
34
What are the X & Y intercepts of the graph y = Tan x
X-intercepts: Kπ Y-Intercepts: 0
35
What are the Domain & Range of graph y = Tan x?
Odd Function Domain: all real numbers except when x = π/2 + kπ Range: (-∞,∞)
36
What are the Period & Asymptotes of the graph y = Tan x?
Period: π Asymptotes: x = π/2 + kπ
37
What are the X & Y intercepts of the graph y = Cot x
X-Intercepts: π/2 + kπ Y-intercepts: None
38
What are the Domain & Range of the graph y = Cot x?
Odd Function Domain: all real numbers except when x = kπ Range: (-∞,∞)
39
What are the Period & Asymptotes of the graph y = Cot x?
Period: π Asymptotes: x = Kπ
40
What are the X & Y intercepts of the graph y = Csc x?
X-Intercepts: None Y-intercepts: None
41
What are the Domain & Range of the graph y = Csc x?
Odd Function Domain: all real numbers except when x = Kπ Range: (-∞,-1] U [1,∞)
42
What are the Period & Asymptotes of the graph y = Csc x?
Period: 2π Asymptotes: x = Kπ
43
What are the X & Y intercepts of the graph y = Sec x
X-Intercepts: None Y-Intercepts: 1
44
What are the Domain & Range of the graph y = Csc x?
Even Function Domain: all numbers except when x = π/2 + kπ Range: (-∞,-1] U [1,∞)
45
What are the Period & Asymptotes of the graph y = Csc x?
Period: 2π Asymptotes: X = π/2 + Kπ
46
What does it mean for a function to be Odd?
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
What does it mean for a function to be Even?
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
What do these functions mean: f(x + h) & f(x - h)?
Transformation: Horizontal Shift- A: f(x + h): Shift left h units B: f(x - h): Shift right h units
49
What do these functions mean: f(x) + k & f(x) - k?
Transformation: Vertical Shift- A: f(x) + k: Shift up k units B: f(x) - k: Shift down k units
50
What do these functions mean: -f(x) & f(-x)?
Transformation: Reflection- A: -f(x): Reflect across x-axis B: f(-x): Reflect across y-axis
51
What do these functions mean: a f(x), a > 1 & a f(x), 0 < a < 1 ?
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
What do these functions mean: f(ax), a > 1 & f(ax), 0 < a < 1 ?
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