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.
What is the value of Sine?
B/C or Opposite over Hypotenuse
What is the value of Cosine?
A/C or Adjacent over Hypotenuse
What is the value of Tangent?
B/A or Opposite over Adjacent
What is the value of Cosecant? What is it the reciprocal of?
C/B or Hypotenuse over Opposite. Is the reciprocal of Sine!
What is the value of Secant? What is it the reciprocal of?
C/A or Hypotenuse over Adjacent. Reciprocal of Cosine!
What is the value of Cotangent? What is it the reciprocal of?
A/B or Adjacent over Opposite. It’s the reciprocal of Tangent.
What is the Reciprocal Identity of Sine?
1/CSC or 1 over Cosecant
What is the Reciprocal Identity of Cosine?
1/SEC or 1 over Secant
What is the Reciprocal Identity of Tangent?
1/COT or 1 over Cotangent
What is the Reciprocal Identity of Cosecant?
1/SIN or 1 over Sine
What is the Reciprocal Identity of Secant?
1/COS or 1 over Cosine
What is the Reciprocal Identity of Cotangent?
1/TAN or 1 over Tangent
What is the Quotient Identity of Tangent?
SIN/COS or Sine over Cosine
What is the Quotient Identity of Cotangent?
COS/SIN or Cosine over Sine
What are the Pythagorean Identities?
a. Sin^2 + Cos^2 = 1
b. Tan^2 + 1 = Sec^2
c. Cot^2 + 1 = Csc^2
What is the Cofunction of Sin B?
Sin B = b/c = Cos A
What is the Cofunction of Cos B?
Cos B = a/c = Sin A
What is the Cofunction of Tan B?
Tan B = b/a = Cot A
What is the Cofunction of Csc B?
Csc B = c/b = Sec A
What is the Cofunction of Sec B?
Sec B = c/a = Csc A
What is the Cofunction of Cot B?
Cot B = a/b = Tan A
What does A.S.T.C. mean?
All Students Take Calculus
A: All Positive
S: Sin/Csc positive
T: Tan/Cot, positive
C: Cos/Sec, positive
What does adjacent turn into?
Adjacent -> X
What does opposite turn into?
Opposite -> Y
What does hypotenuse turn into?
Hypotenuse -> R
What is the equation for R?
R = √x^2 + y^2
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
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
What are the Domain & Range of graph y = Sin x?
Odd Function
Domain; (-∞,∞)
Range: [-1,1]
What are the Period & Amplitude of graph y = Sin x?
Period: 2π
Amp: 1
What are the X & Y intercepts of the graph y = Cos x?
X-intercepts: π/2 + Kπ
Y-intercepts: 1
What are the Domain & Range of the graph y = Cos x?
Even Function
Domain(-∞,∞)
Range: [-1,1]
What are the Period & Amplitude of graph y = Cos x?
Period: 2π
Amp: 1
What are the X & Y intercepts of the graph y = Tan x
X-intercepts: Kπ
Y-Intercepts: 0
What are the Domain & Range of graph y = Tan x?
Odd Function
Domain: all real numbers except when x = π/2 + kπ
Range: (-∞,∞)
What are the Period & Asymptotes of the graph y = Tan x?
Period: π
Asymptotes: x = π/2 + kπ
What are the X & Y intercepts of the graph y = Cot x
X-Intercepts: π/2 + kπ
Y-intercepts: None
What are the Domain & Range of the graph y = Cot x?
Odd Function
Domain: all real numbers except when x = kπ
Range: (-∞,∞)
What are the Period & Asymptotes of the graph y = Cot x?
Period: π
Asymptotes: x = Kπ
What are the X & Y intercepts of the graph y = Csc x?
X-Intercepts: None
Y-intercepts: None
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,∞)
What are the Period & Asymptotes of the graph y = Csc x?
Period: 2π
Asymptotes: x = Kπ
What are the X & Y intercepts of the graph y = Sec x
X-Intercepts: None
Y-Intercepts: 1
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,∞)
What are the Period & Asymptotes of the graph y = Csc x?
Period: 2π
Asymptotes: X = π/2 + Kπ
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)
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)
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
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
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
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
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
