Graphing Sine & Cosine

What are the five critical values for the sine and cosine parent functions?

What effect does |a| have on the parent graph?

$$y=a\sin\left[b\left(x-h\right)\right]+k$$

Which characteristic does |a| affect?

$$y=a\sin\left[b\left(x-h\right)\right]+k$$

What effect does a being negative have on the parent graph?

$$y=a\sin\left[b\left(x-h\right)\right]+k$$

Which characteristic is affected if a is negative?

$$y=a\sin\left[b\left(x-h\right)\right]+k$$

Match the equation to the shape of its graph from 0 to 2π.

What effect does k have on the parent graph?

$$y=a\sin\left[b\left(x-h\right)\right]+k$$

Which characteristic does k affect?

$$y=a\sin\left[b\left(x-h\right)\right]+k$$

Identify the key characteristics: $$y=\frac{1}{2}\cos x-3$$

Midline:​ (a)  

Amplitude:​ (b)  

Period:​ (c)  

Identify the shape of the graph: $$y=\frac{1}{2}\cos x-3$$