6.2 Proving Trigonometric Identities Proofs (I)
Tuesday, April 16, 2013
Review: Simplify: (secx cscx cotx)(sinx cscx)
Since numerical substitution does not ensure an identity, we must
use a proof method in showing trig identities.
Steps for proofs
Set u
5.6 Properties of Linear Functions (II)
Monday, February 21, 2011
10:48 AM
Linear Function
Constant change in independent variable results in
a constant change of the dependent variable.
When graphed forms a _
Rate of change (slope)
= _
Examples:
1. D
6.4 Applications of Linear Functions
Thursday, April 04, 2013
10:17 AM
Review: Determine the equation, in standard form, of a line which
is perpendicular to 4x + 5y 4 = 0 and shares the same y-intercept
as 3x 4y = 8
Linear appreciation: value increases by
6.5 Double Angle Identities
Wednesday, May 01, 2013
3:02 PM
Sin2x = _
Proof: sin2x = 2sinxcosx
cos2x = _
Proof: cos2x = cos2x sin2x
Other forms of Cos2x
The 3 versions of cos2x:
Trigonometry (II) Page 1
tan2x =
Examples:
1. Write 10sin3xcos3x as a single
6.1 Reciprocal, Quotient and Pythagorean Identities
Wednesday, April 10, 2013
2:53 PM
Trigonometric equations are TRUE for _ values of the variable.
Trig identities are TRUE for _ values of the variable
Trigonometry (II) Page 1
Trigonometry (II) Page 2
6.4 The Graphing Calculator
QUIZ to start (6.1 6.4)
2 Methods for solving quadratics using a graph. calc.
Solve 2x2 x = 3
1. Use intersection function
2. Finding zeros of graph
Press <2nd>, <Calc>
Arrange eq to 2x2 x 3
#5 (intersection)
Press <2nd>,
5.1 Language of Math
Tuesday, November 15, 2011
1:46 PM
2
3x + 2x 5
Monomial:
Binomial:
Trinomial:
Leading coefficient
Degree of polynomial / term:
SUM of exponents on the variable(S) of a monomial
New Section 1 Page 1
In a polynomial you find the
6.1 Slope Point Form (II)
Thursday, March 17, 2011
1:44 PM
Review: Determine the equation of a line with a slope of 3/4 and
goes thru the point (8, 1)
Not all equations of lines are written in slope intercept form
(y = mx + b).
Another form is called sl
6.1 General and Standard Form of Linear Equation (III)
Wednesday, April 06, 2011
1:30 PM
Review: Write in slope-intercept form: y 3 = 3/4(x + 2)
Different ways to write the equation of the line
Slope intercept form:
_
Slope point form
_
Standard form:
_
G
7.1 Graphing Non-Linear Systems of Equations
Wednesday, May 02, 2012
9:35 AM
System:
2 or more equations
Linear (first degree y = 2x + 3)
Quadratic (2nd degree y = x2)
The solution is the _
Coordinates must satisfy _ equations
Number of Solutions of
7.1 Fundamental Counting Principle
Tuesday, April 10, 2012
11:37 AM
To develop systematic ways of counting
1. A caf serves egg or ham sandwiches; milk, juice, or coffee; and
yogurt of cake for dessert as a special.
a) Use a tree diagram to list all possi
6.2 Solving Quadratic Equations by Completing the Square
Tuesday, October 14, 2008
1:26 PM
Review: Solve and check (x + 7)(x + 3) = (x + 7)(5 x)
COMPLETING THE SQUARE is a technique that can be used to
solve quadratic equations that cannot be easily fact
7.3 Graphing Linear Inequalities (II)
Tuesday, May 01, 2012
8:29 AM
Review: Graph y < 2x + 5 and y > 3x 2 on the same grid
Graphing System of Linear Inequalities
Combine the graphs of the individual inequalities and
look where both regions overlap.
This
5.4 Graphing Sin and Cos Functions (I)
Monday, February 25, 2013
10:47 AM
Review: Complete the chart (no calcs). (Use radians)
Trigonometry (I) Page 1
Graphing Trig Function Vocab
Cycle:
Period
Amplitude:
Properties of sinx and cosx
Sinx
Cosx
Amplitude:
A
6.3 Solving Trigonometric Equations (no technology)
Wednesday, April 24, 2013
8:34 AM
Review: solve 2x2 x = 3
Trig equations can be solved much the same way
Remember
to identify the sign of the trig ratio
Examples:
1. Solve sinx = 0.75
2. Solve for x in
5.5 Applications of Periodic Functions
Thursday, October 27, 2011
12:33 PM
Example 2:
A Ferris wheel has a radius of 10m and the maximum height the chair reaches is 22m. The
wheel takes 90 seconds to complete one revolution.
a) Sketch a graph that represe
5.6 Applications of Quadratics (Max/Min Problems)
Wednesday, February 01, 2012
8:28 AM
1. Two numbers have a sum of 24. Their product is a maximum.
What are the numbers?
2. Find two numbers that have a difference of 18 and a product that
is a minimum.
3.
5.2/5.3 Graphing y = a(x p)2 + q (II)
Wednesday, October 31, 2007
7:37 PM
Review: Graph without using a table
2. Y = x2 + 2
1. Y = 3x2 6
Vertex:
Pattern:
Examples:
1. Graph y = x2 without using a table of values
vertex
pattern
Opens:
Quadratic Functions P
5.4 Slopes of Parallel and Perpendicular Lines
Wednesday, March 09, 2011
10:30 AM
Review: determine the value of m, such that a line passes thru
(5, m) and ( 3, 4) with a slope of 3/4
Activity:
on your grid paper draw graph with a slope of 2/3 thru the o
5.3 Trig Function General & Special Angles
Monday, February 25, 2013
10:21 AM
Reference angle: the positive acute angle formed between
the terminal arm and the x-axis.
Quadrant Angles
sin
csc
cos
Special Angles
Trigonometry (I) Page 1
sec
tan
cot
sin
cs
5.3 Interpreting and Sketching Graphs (TEXT)
Tuesday, February 08, 2011
10:40 AM
Review: For the function f(x) = 3x 4 determine
a) f( 1)
b) f(4)
c) f(x) = 11
Graphs can provide much information
Look at title, and axis labels to gather as much info as po
5.4/5.5 Graphing y = ax2 + bx + c (complete the square)
Tuesday, November 06, 2007
9:55 AM
Review: Draw a graph for y = 1/2 (x 1)2 + 4
a) vertex
c) opens?
b) pattern
d) max or min value
Standard form of quadratics: y = a(x p)2 + q
General form
: y = ax
7.3 Combinations
Wednesday, May 22, 2013
10:29 AM
1. If 5 runners compete in a race, in how many different ways can
1st, 2nd, 3rd be awarded?
Does the order matter here?
This is an example of a _ of _ objects taken _ at
a time.
2. What if the fastest 3 qu
7.1 Tables
Thursday, May 14, 2015
9:23 AM
1. Mr G's math class took a quiz last week and the following are the
students' scores with a total mark out of 10. (there were 20
students)
6 8 3 4 9 6 10 6 8 9 4 6 7 10 6 6 8 5 6 7
a) Complete a frequency table
b
7.2 Solving Non-Linear Systems Algebraically
Tuesday, May 01, 2012
9:33 AM
Review: draw a quadratic - quadratic system which has a infinite
solutions (called coincident).
1.
2.
3.
4.
5.
Steps to solving algebraically
Write equations in terms of y
Substitu
6.1 Solving Quadratic Equations by Factoring
Thursday, October 09, 2008
2:06 PM
A quadratic equation has the form of ax2 + bx + c = 0. When you
solve a quadratic, you find the values of x that make the equation
true.
Examples:
1. x2 3x + 2 = 0
3. 6x2 7x