### Home > PC3 > Chapter 4 > Lesson 4.1.1 > Problem4-20

4-20.

​ Graph each of the following trigonometric functions. Describe the transformation.

1. $y=2\sin\left(x-\frac{\pi}{4}\right)+1$

1. $y=-3\cos(2x)-2$

1. $y=3-\sin(x)$

$y=a\sin(b(x−h))+k$
$a=$ amplitude
$\frac{2\pi}{b}=$ period
$h=$ horizontal shift
$k=$ vertical shift

Do not use a calculator! Sketch a prediction of what you think the curve looks like.
Then, use a graphing calculator to check your prediction. Correct any errors you might have made.
Remember that making mistakes and identifying and correcting them is how you build brain cells.