How to #1
How to sketch sine and cosine graphs
How to sketch sine and cosine graphs
The Basics;
.gif)
\[\\\frac{2\pi}{n} \ \text{is the period} \\a \ \text{is the amplitude} \\c \ \text{is the horizontal transformation (graph is translated -c units)} \\b \ \text{is the vertical transformation}\]
Sketching a sine graph which has been vertically translated
We can see here that the amplitude is 2
There is a vertical translation of 3 units up
And that the period is
a) Divide the period by 4; $\frac{\pi}{4}$
b) Multiply a) by 2; $\frac{\pi}{2}$
c) Multiply a) by 3; $\frac{3\pi}{4}$
We now have 4 parts, however, as the domain is \[0\leq x\leq 2\pi\]. We need to add $\pi$ to each part
$\frac{\pi}{4}$+&\pi&=&\frac{5\pi}{4}$
$\frac{\pi}{2}+\pi=\frac{3\pi}{2}$
$\frac{3\pi}{4}+\pi=\frac{7\pi}{4}$
$\pi+\pi=2\pi$
.gif)
\[\\\frac{2\pi}{n} \ \text{is the period} \\a \ \text{is the amplitude} \\c \ \text{is the horizontal transformation (graph is translated -c units)} \\b \ \text{is the vertical transformation}\]
We can see here that the amplitude is 2
There is a vertical translation of 3 units up
And that the period is
a) Divide the period by 4; $\frac{\pi}{4}$
b) Multiply a) by 2; $\frac{\pi}{2}$
c) Multiply a) by 3; $\frac{3\pi}{4}$
We now have 4 parts, however, as the domain is \[0\leq x\leq 2\pi\]. We need to add $\pi$ to each part
$\frac{\pi}{4}$+&\pi&=&\frac{5\pi}{4}$
$\frac{\pi}{2}+\pi=\frac{3\pi}{2}$
$\frac{3\pi}{4}+\pi=\frac{7\pi}{4}$
$\pi+\pi=2\pi$
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