## Thursday, February 17, 2011

### Graph Sine and Cosine using GEOGEBRA

You should print this worksheet, see below,  or you can make up your own functions to study.
Then click link to go to the Graphing ACTIVITY.

Graphing Sine and Cosine Functions with Variations

Worksheet for Graphing Sine and Cosine:
Use pencil and paper to copy each of these graphs that Geogebra will create for you.
You should have 12 separate graphs.
Can you predict the graph changes?
Try some yourself.     If you use  y=2sin(x)  what graph will you have?
Change the 2 to 3 or -3, what happens to the graph.  The amplitude changes.
Try other combinations.     y=sin(2x). This 2 will affect the period of the function rather than the amplitude.

1. SINE function
A. period=2pi amplitude = 3 Equation_________
B. period=2pi amplitude = 3 up 3 Equation_________
C. period=2pi amplitude = 3 up 3 left pi/4 Equation_________
D. Complete each graph and also state the "5 points" for B. and C. on the graph.
Does your graph match the info I gave you for C? I hope so HOW can you know for sure?
2. SINE function
A. period=pi amplitude = 3 Equation_________
B. period=pi amplitude = 3 down 1 Equation_________
C. period=pi amplitude = 3 down 1 right pi/2 Equation_________
D. Complete each graph and also state the "5 points" for B. and C. on the graph.
3. COSINE function
A. period=2pi amplitude = -2 Equation_________
B. period=2pi amplitude = -2 up 1 Equation_________
C. period=2pi amplitude = -2 up 1 right pi/4 Equation_________
D. Complete each graph and also state the "5 points" for B. and C. on the graph.
4. COSINE function
A. period= 4pi amplitude = 3 Equation_________
B. period=4pi amplitude = 3 down 2 Equation_________
C. period=4pi amplitude = 3 down 2 right pi/3 Equation_________
D. Complete each graph and also state the "5 points" for B. and C. on the graph.

Let me know if you need help.       If you need the equations then email me.  Be specific in you request as I have many online students studying different topics.
Susan Johnsey  sjohnsey at bellsouth dot net

## Sunday, February 6, 2011

### Email request for solving linear equations

Hi   johnsey, I have a hard time figuring out solving 2 math problems.
Here they are:
5y - 3 = 8 + 4(y - 2) and   if 7x + 3 = 5x - 5, evaluate 2x - 1.

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5y - 3 = 8 + 4(y - 2)  Multiply on right side and add LIKE terms  then solve.
5y-3 = 8+4y-8       the 8-8 is 0 so we get
5y-3 =4y      Since the only number term, the -3, is on the left side I will move the y-terms to the right.   Subtract 5y from both sides.
5y-3 -5y =4y -5y

-3  = -y   Now we want to finish with y or +1y  so divide both sides  by -1.
-3/-1 = -y/-1   thus we  get y = 3.

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If 7x + 3 = 5x - 5, evaluate 2x - 1.

Solve for x first then we evaluate.
7x + 3 = 5x - 5 I will move the variable terms to the left side and the number terms to the right.
subtract 5x from both sides.
7x + 3 -5x = 5x - 5 -5x

2x+3 = -5   Now subtract 3 from both sides.
2x+3-3 = -5-3
2x=-8   so x =  - 4.

now evaluate 2x - 1. let x=-4 we get 2(-4) -1 -8-1 = -9.   The -9 is the answer.