ITT Technical Institute Norwood campus, Norwood OH
MA 1310

Summer 2014
Quiz 2.1 Prep
MA1310
Logarithm Rules
Logarithmic
form:
Exponential
form:
y log b x
y
b x
Product Rule:
log b ( MN )
log b M log b N
M
) log b M log b N
Quotient Rule: log b (
N
Power Rule:
Change of
Base:
P
log b M p log b M
log M
log b M
log b
ln M
or l
ITT Technical Institute Norwood campus, Norwood OH
MA 1310

Summer 2014
1. State in a few words, what is an exponential function?
a. An exponential function is a mathematical expression in which a variable
represents the exponent of an expression.
2. What is the natural exponential function?
a. f(x) =ex where
e is Eulers numb
ITT Technical Institute Norwood campus, Norwood OH
MA 1310

Summer 2014
Quiz 4.1 Prep Part 1
MA1310
Unit Circle Guide
Properties Of Trig Graphs
Domain
The domain of the sine AND the cosine
function will always be :
(,)
This means that the x values we plug into the
sine and cosine function can be anything, no
restrictions!
De
ITT Technical Institute Norwood campus, Norwood OH
MA 1310

Summer 2014
Quiz 10.1 Prep
MA1310
Sequence Formulas
General Term of Arithmetic
Sequence: a a ( n
n
1
1)d
Sum of the First n Terms of Arithmetic Sequence:
n
S n (a1 an )
2
General Term of Geometric Sequence:
an a1r n 1
Sum of the First n Terms of Geometric Sequence:
ITT Technical Institute Norwood campus, Norwood OH
MA 1310

Summer 2014
Quiz 4.1 Prep Part 2
MA1310
Solve Using Periodic Property
As you have noticed, the graphs of trigonometric functions repeat to infinity.
With this said, we can find values of trig functions using the periodic
property:
sin(t 2 n) sin t
cos(t 2 n) cos t
22
ITT Technical Institute Norwood campus, Norwood OH
MA 1310

Summer 2014
MA1310:Week5LawofSinesandCosines
1. Define the Law of Sines.
a. THE LAW OF SINES allows us to solve triangles that are not rightangled,
and are called oblique triangles. It states the following: The sides of a
triangle are to one another in the same rati
ITT Technical Institute Norwood campus, Norwood OH
MA 1310

Summer 2014
MA1310:Week2SolvingExponentialandLogarithmicEquations
1. Solve the exponential equation by expressing each side as a power of the
same base and then equating exponents.
x
6 = 216
3
6 =216
The solution set is cfw_3
2. Solve the exponential equation. Expres
ITT Technical Institute Norwood campus, Norwood OH
MA 1310

Summer 2014
Week 5 Prep
MA1310
Law of Sines/Cosines
Angles of a triangle:
A B C 180
Law of Sines:
a
b
c
sin A sin B sin C
Law of Cosines:
a b 2 c 2 2bc cos A
b a 2 c 2 2ac cos B
c a 2 b 2 2ab cos C
Calculator Hints:
If you are trying
to find the
inverse sine or
cosin
ITT Technical Institute Norwood campus, Norwood OH
MA 1310

Summer 2014
This Sinusoidal graph will show the depth of water at the end of a dock in Bar Harbor, Maine
throughout the day. The table shows the depths (in feet) at various times during the morning.
(Source: Nautical Software, Inc.)
The cosine model of the form
y = a
ITT Technical Institute Norwood campus, Norwood OH
MA 1310

Summer 2014
A typical problem that requires the use of the Law of Cosines in order to solve it involves a
triangle in which there is no right angle. We are given some information about a triangle, but we
have to find measurements of other sides and/or angles. The Law
ITT Technical Institute Norwood campus, Norwood OH
MA 1310

Summer 2014
The Physics example that I have chosen to describe the Dot Product of Vectors is:
Definition of Work is the energy needed to move an object by a force. If the force is expressed as
a vector F and the displacement a vector D, the work is
W = F Dcos
Where
ITT Technical Institute Norwood campus, Norwood OH
MA 1310

Summer 2014
How many were going to St. Ives? Just me, one person
How many kittens are being transported? 2,401
Kits, cats, sacks, wives; how many? 2,800
The sequence is 7meaning:
7 wives
72 = 49 sacks
73 = 343 cats
74 = 2401 kittens
For a reallife application exampl
ITT Technical Institute Norwood campus, Norwood OH
MA 1310

Summer 2014
Finding a Force (Work)
A 200 lb gocart sits on a ramp inclined at 30o. What force is required to keep the cart from
rolling down the ramp?
(Force required = magnitude of the Work)
F = 200j
Because the force due to gravity is vertical and downward, you ca
ITT Technical Institute Norwood campus, Norwood OH
MA 1310

Summer 2014
Solving a SSA Triangle:
Example:
Solution:
Suppose c = 10, a = 16.38, and C = 30o. Solve the triangle ABC.
The triangle shows that we are given two sides and an angle not contained between the
given sides. Apply the law of sines to the known information.
ITT Technical Institute Norwood campus, Norwood OH
MA 1310

Summer 2014
MA1310:Week6PolarCoordinatesandComplexNumbers
This lab requires you to:
Plot points in the polar coordinate system.
Find multiple sets of polar coordinates for a given system.
Convert a point from polar to rectangular coordinates.
Convert a point from rec
ITT Technical Institute Norwood campus, Norwood OH
MA 1310

Summer 2014
1.
This graph showing the DJIA from 19452000 is a Line Graph
2.
This graph showing the DJIA from 19802000 represents an exponential function type graph.
3.
If we had invested $10,000 in 2000, we can expect to have about $33,000 in 2010 by
extrapolating