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5.1
(Trigonometric Equations)
Relating Graphs and Solutions
5.2
Example for 1-9:
Use the graph of y = Sinx to help find the exact
solutions of Sinx = -1. (h. scale is /2)
Solving Trigonometric Equations
Sin(+)
Cos()
Tan()
Sin()
Cos()
Tan(+)
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2.2
(Exponents & Logarithms1)
Laws of Logarithms
Extrapolate off of the graph
y = Abx, A is a constant
Example for 10-12:
1
Find the approximate value of (3)x = 15.
Example for 1-3:
Use the graph of y = 3x to find the approximate value
of 32.
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2.6
Laws of Logarithms
Log of a Product:
Log of a Quotient:
Log of a Power:
Log of a Root:
logbxy = logbx + logby
x
logb = logbx logby
y
logbxn = nlogbx
n
logb x = logbx
1
n
Example for 1-10:
Write as a single logarithm and evaluate.
log25 +
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1.1
Horiz. & Vert. Translations of Functions
Given y = f(x):
y = f(xh)
y = f(x+h)
y = f(x)k
y = f(x)+k
-> moves function h units right,
-> moves function h units left,
-> moves function h units down,
-> moves function h units up.
(Transformat
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3.5
The Hyperbola
x2 y2 = a2
center (0, 0), vertices = (a, 0), (-a, 0)
(x h) 2 (y k) 2
= 1
Hyperbola:
a2
b2
center (h, k), transverse axis = 2a, conjugate axis = 2b
Rectangular Hyperbola:
Example for 1-5:
Find the center, length of axes, vert
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1.6
Combinations of Transformations
(Transformations2)
Example for 26-31:
1. y = x2
Given y = f(x): y = af(xh) + k
moves function h units horizontally,
moves k units vertically,
multiplies y values by a,
divides x values by b.
Example for
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4.4
(Trigonometric Functions2)
Further Transformations of Sin & Cos
y = aSinb(x h) + k
y = aCosb(x h) + k
a = amplitude (vertical stretch)
b = period (horizontal stretch)
h = phase shift (horizontal transformation)
k = vertical displacement (
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5.4
Trigonometric Identities
Sin2x + Cos2x = 1
Sinx
Tanx =
Cosx
(Trigonometric Identities)
1 + Tan2x = Sec2x
1
Secx =
Cosx
1 + Cot2x = Csc2x
1
Cscx =
Sinx
Change to Sin & Cos only
Simplify Complex Fractions
Multiply out ( )
Factor common fac
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4.1
(Trigonometric Functions1)
Angular Measure
180
Radians
arc length
=
2
circumference
Radians = Degrees x
180
Degrees
arc length
=
360
circumference
Degrees = Radians x
Example for 41-46:
Is 165 coterminal with 525?
165 + n = 525
n = 525 16
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3.3
The Circle
Basic equation:
Translated equation:
x2 + y2 = r2
center (0, 0), radius = r
(x h)2 + (y k)2 = r2
center (h, k), radius = r
Example for 1-8:
Write an equation with center (0, 0) & radius 7
x2 + y2 = r2
x2 + y2 = 72
x 2 + y2 = 49