1. Warm Up
Get your Spaghetti Sine projects off the shelf and return to your partner. Do not continue working on the project, rather, answer the questions on the instruction sheet to the best of your ability.

2. Graphing Trig Functions

3. Sine Graph of y = sin(x) Starts at the origin. 1 -4π -3π -2π -π π 2ππ 2π 3π 4π
Starts at the origin. -1

4. Cosine Graph of y = cos(x) Starts at the max. 1 -4π -3π -2π -π π 2π 3ππ 2π 3π 4π -1

5. The period of y = sin(x) is 2π!
The period of a function is the length of the piece of the graph that repeats itself. π 2π 3π 4π 5π 6π
The period of y = sin(x) is 2π!

6. Find the period of each graph:π 2π 3π 4π 5π 6π π 2π 3π 4π 5π 6π π 2π 3π 4π 5π 6π

7. Amplitude Amplitude is the distance from the midline to the maximum. 1
Always measure the amplitude from “sea level.”
Sea level changes as the center of the graph moves up and down. 1
-4π
-3π
-2π -π π 2π 3π 4π -1

8. Find the amplitude of each graph:1 -1 π 2π 3π -2 5 -3 π 2π 3π π 2π 3π
-16

9. Sine vs. Cosine Graphs Both graphs have a period of 2π.1
-4π
-3π
-2π -π π 2π 3π 4π -1
y = sin(x) starts at 0.
Both graphs have a period of 2π.
Both graphs have an amplitude of 1. 1
y = cos(x) starts at 1.
-4π
-3π
-2π -π π 2π 3π 4π -1

10. y = asin(bx) y = acos(bx)
Amplitude of the graph = a Period of the graph =
b is called the frequency.

11. Example 1: Determine the period and amplitude of each trig function:
y = 7cos(2x)
y = -8sin(3x)
y = ¼cos(6x)
y = -sin(πx)

12. Example 2: Determine the period and amplitude of the function
Example 2: Determine the period and amplitude of the function. Then, graph it!
y = 5sin(2x)

13. Example 3: Determine the period and amplitude of the function
Example 3: Determine the period and amplitude of the function. Then, graph it!
y = ⅔cos(4x)

14. Example 4: Determine the period and amplitude of the function
Example 4: Determine the period and amplitude of the function. Then, graph it!
y = -16sin(x)