Math 152 Sec S0601/S0602
Extra Trigonometry Problems II
Problems
bh
. With
2
reference to the triangle below (not necessarily a right triangle), nd a formula for the area
A which is in terms of , a and b.
1. Recall that the area of a triangle is given as
Math 152 Sec S0601/S0602
Notes on Binomial Theorem and Sequences
1
1.1
The Binomial Theorem: Another Approach
Pascals Triangle
In class (and in our text) we saw that, for integer n 1, the binomial theorem can be stated
(a + b)n = c0 an + c1 an1 b + c2 an2
Math 152 Sec S0601/S0602
Notes Matrices IV
5
Inverse Matrices
5.1
Introduction
In our earlier work on matrix multiplication, we saw the idea of the inverse of a matrix. That is,
for a square matrix A, there may exist a matrix B with the property that AB =
Math 152 Sec S0601/S0602
Extra Trigonometry Problems
Problems
Graph the following trigonometric functions over [P, P ] where P is the period of the function.
Determine the period, phase shift and amplitude.
1. f (x) = cos x +
2. y =
2 .
4
x
1
sin
2 .
2
2
Math 152 Sec S0601/S0602
Notes Matrices II
3
Matrix Multiplication
3.1
Introduction
So far we have seen two algebraic operations with matrices, addition and scalar multiplication, and
we have also seen how the zero matrix plays a role in these operations
Math 152 Sec S0601/S0602
Notes on Series
1
Series
Now that we have studied sequences in general, and arithmetic and geometric sequences in particular, we make use of these to dene the notion of a series. Given a sequence
cfw_an = a1 , a2 , a3 , . . .
n=1
Math 152 Sec S0601/S0602
Notes Matrices III
4
4.1
Solving Systems of Equations by Reducing Matrices
Introduction
One of the main applications of matrix methods is the solution of systems of linear equations.
Consider for example solving the system
2x 3y =
Math 152 Sec S0601/S0602
Notes on Matrices
1
1.1
Matrices: Introduction, Terminology, Notation
Introduction
Consider the problem of solving the system of equations
x 2y = 1
2x + 3y = 2
(1)
(2)
We can do this easily using substitution: use equation (1) to