Section 6-5
symmetry for polar graphs
analyzing a polar graph
finding maximum r-values
rose curves
limaon curves
other polar graphs
Limaon Curves
format r = a b sin
or r = a b cos
range is [a b, a + b]
with cos then x-axis symmetry
with sin then y-ax
Section 6-5
symmetry for polar graphs
analyzing a polar graph
finding maximum r-values
rose curves
limaon curves
other polar graphs
Symmetry For Polar Graphs
x-axis:
r = 6 cos
Symmetry For Polar Graphs
y-axis:
r = 4 + 4sin
Symmetry For Polar Graphs
o
Equation Conversion
equations in polar form have r in terms of
example : r = 4cos
these equations can be graphed using
the calculator or by hand
to convert equations between
rectangular form and polar form use:
x = r cos
y = r sin
r =x +y
2
2
2
Conv
Section 6-4
polar coordinate system
negative r-values
finding all polar coordinates of a point
coordinate conversion
polar equations
equation conversion
distance between polar coordinates
Polar Coordinates
a different system of plotting points and
coordi
Projectile Motion
simulating projectiles shot straight up
x=t
y = -16t2 + v0t + y0
v0 = initial velocity y0 = initial height
this shows the height against time, if you want
it to look like its going straight up and down,
use x = 5 instead of x = t
Simul
Section 6-3
parametric equations
graphing parametric equations
eliminating the parameter
finding the parametrization of a line
simulating projectile motion
simulating circular motion
Parametric Equations
ordered pairs (x , y) are based upon a
third variab
A sled is sitting on the side of a hill inclined at 45.
The weight of the sleigh and its contents is 140 lbs.
What force is required to keep the sled from sliding
down the hill?
Work
if an object is moved from point A to point
B by a force, F, then we ca
Section 6-2
the dot product
finding the angle between two vectors
orthogonal vectors
projection of a vector onto another
vector
work problems
The Dot Product
the dot product of a vector has many
physical and geometric applications
you cannot multiply t
Unit Vectors
a vector with magnitude of 1 is called a
unit vector
to find a unit vector, u, in the direction
of a vector v, use:
v
u=
v
there are two standard unit vectors:
i = 1, 0
and
j = 0, 1
Find a unit vector in the direction of v = 2, 3
Direction of
Section 6-1
directed line segments and vectors
equal vectors
component form of a vector
magnitude of a vector
vector operations
unit vectors
direction of a vector
applications
Directed Line Segments
some quantities, such as force, velocity,
and accelerati
Infinite Series
when an infinite number of terms are added
together the expression is called an
infinite series
an infinite series is not a true sum (if you
add an infinite number of 2s together
the sum is not a real number)
yet interestingly, sometime
Sequences
a sequence is an ordered progression of
numbers
they can be finite (a countable # of terms)
or infinite (continue endlessly)
a sequence can be thought of as a function
that assigns a unique number an to each
natural number n
an represents th
Binomial Distribution
used for probability with n independent
repetitions of an experiment with two
outcomes, called success and failure
P(success) = p and P(failure) = q
let r be the number of successes out of
n attempts, its probability is:
n r nr
Binomial Expansion
expanding (a + b)4 by repeatedly using the
distributive property would be a very
time consuming process
this can be made easier by using the
Binomial Theorem which will be
introduced in this section
this theorem will make expansions
Section 8-3
the geometric definition of a hyperbola
standard form of a hyperbola with a
center at (0 , 0)
translating a hyperbola center at (h , k)
graphing a hyperbola
finding the equations of the asymptotes
finding the equation of a hyperbola
ecc
Section 8-2
the geometric definition of an ellipse
standard form of an ellipse with a
center at (0 , 0)
translating an ellipse center at (h , k)
graphing an ellipse
finding the equation of an ellipse
eccentricity and orbits
reflective property of a
Section 8-1
the conic sections
definition of parabola
standard form of the equation of a parabola
translating a parabola
graphing a parabola
convert from general form to standard form
reflective property of parabolas
Parabola: the set of all points equidi
Section 5-6
Law of Cosines & Area
Section 5-6
the Law of Cosines
solving triangles (SSS and SAS)
finding the area of a triangle (SAS)
Herons Formula (Area of SSS)
applications
Law of Cosines
used to find the missing parts of triangles
if you are given SSS
Section 5-5
solving non-right triangles
Law of Sines
solving triangles AAS or ASA
solving triangles SSA
Applications
Solving Non-Right Triangles
In Chapter 4 we learned to solve right
triangles, which meant that we could find all
its missing parts
In the
Section 5-4
double-angle identities
power-reducing identities
half-angle identities
solving trig equations (again)
Double-Angle Identities
Prove the identity : sin 2u = 2 sin u cos u
Power-Reducing Identities
1
Prove the identity : cos x = (3 + 4 cos 2 x
Section 5-3
Sum and Difference Identities
Section 5-3
cosine of a sum or difference
sine of a sum or difference
tangent of a sum or difference
expressing the sum of sinusoid as a sinusoid
Cosine of a Sum or Difference
a very common error when working with
Honors Pre-Calc.
Polar Graphs
Sketch the graph on polar graph paper without a calculator
1.)
r = 4 cos
2.)
r = 3 5sin
3.)
r = 5sin 3
4.)
r = 3 + 3cos
5.)
r = 5 csc
6.)
r = 8 cos 2
Write the polar equation of the curve.
7.)
8.)
Section 10-3 Limits
informal definition of limit
properties of limits
limits of continuous functions
one-sided limits and discontinuous
functions
limits involving infinity
Informal definition of limit
lim f ( x ) = L
x a
means that f(x) gets close to L