Make a word document with the key points (in tables/charts) for the following functions, given in the form y=asink(x+d)+c
Start with multiplication/division (multiply ‘y’ by a, divide ‘x’ by k)
Then add c to the y values, subtract d from the x values
1.y=3sinx+2
2.y=1/2sin(x-180)
3.y=sin(20x+180)
4.y=sinx +7
5.y=sin(x+30)-2
and what do you want us to help you with?
What is the number that I am thinking of if I multiply it by 9 then divide it by 6 then multiply it by 8 then divide it by 4 and the answeer is 12.78 what's the answer
I didn't get the answer I wanted so make Dr. Abbas put the answer on board.
To create a Word document with the key points for the given functions in the format y=asink(x+d)+c, we'll start by applying the necessary transformations to the functions. Then, we'll list the key points using tables/charts. Here's how you can do it:
1. Applying multiplication/division (multiply ‘y’ by a, divide ‘x’ by k):
a) y = 3sinx + 2: Multiply 'y' by 3 → y = 3 * 3sinx + 2 * 3 → y = 9sinx + 6.
Key Points (x, y):
<table>
<tr>
<th>x</th>
<th>y</th>
</tr>
<tr>
<td>0</td>
<td>6</td>
</tr>
<tr>
<td>π/2</td>
<td>9</td>
</tr>
<tr>
<td>π</td>
<td>6</td>
</tr>
<tr>
<td>3π/2</td>
<td>3</td>
</tr>
<tr>
<td>2π</td>
<td>6</td>
</tr>
</table>
2. Applying multiplication/division and addition/subtraction (divide 'x' by k, subtract d from 'x'):
b) y = 1/2sin(x - 180): Divide 'y' by 2 and subtract 180 from 'x':
y = 1/2 * sin(x - 180) → y = 1/2sinx - 1/2sin(180) → y = 1/2sinx - 1/2 * 0 → y = 1/2sinx.
Key Points (x, y):
<table>
<tr>
<th>x</th>
<th>y</th>
</tr>
<tr>
<td>180</td>
<td>0</td>
</tr>
<tr>
<td>180 + π/2</td>
<td>1/2</td>
</tr>
<tr>
<td>180 + π</td>
<td>0</td>
</tr>
<tr>
<td>180 + 3π/2</td>
<td>-1/2</td>
</tr>
<tr>
<td>180 + 2π</td>
<td>0</td>
</tr>
</table>
3. Applying multiplication/division and addition/subtraction:
c) y = sin(20x + 180): Multiply 'x' by 20 and add 180 to 'x':
y = sin(20x + 180).
Key Points (x, y):
<table>
<tr>
<th>x</th>
<th>y</th>
</tr>
[Add the key points here]
4. Applying addition/subtraction:
d) y = sinx + 7: Add 7 to 'y':
y = sinx + 7.
Key Points (x, y):
<table>
<tr>
<th>x</th>
<th>y</th>
</tr>
[Add the key points here]
5. Applying addition/subtraction and multiplication/division:
e) y = sin(x + 30) - 2: Add 30 to 'x' and subtract 2 from 'y':
y = sin(x + 30) - 2.
Key Points (x, y):
<table>
<tr>
<th>x</th>
<th>y</th>
</tr>
[Add the key points here]
You can copy the tables and paste them into a Word document, then add the respective function and key points next to each table.