## Graphs Dealing with Sine and Cosine Problems

#### Aligned To Common Core Standard:

**High School Geometry** - HSG-SRT.D.10

What Are the Characteristics of Graphs of Sine and Cosine Functions? Recall that the sine and cosine function relating to real number values to the two coordinates x and y to the point of the unit circle. So how would they look like on a coordinate plane graph? Let's start with the basic sine functions. We can create a values table and using them for sketching a graph. Plotting points from the table in a continuous manner along the x-axis gives the shape of the sine function. You can see how the sine values on the graph above have values between 0 and pie. These values correspond to the value of the sine functions lying within the quadrants 1 and 2 of the unit circle. The sine values are negative between pie and 2pie, corresponding to the sine function values in the 3rd and 4th quadrant on the circle. These worksheets and lessons help students learn how to read and interpret graphs that include the sine and cosine functions.

### Printable Worksheets And Lessons

- Graphing Waves Step-by-Step Lesson- I'm a surfer. I would rather ride waves than graph them.
- Guided Lesson - Graph the sine and cosine equations and then find the equation of another wave.
- Guided Lesson Explanation - The first two are pretty straight forward. I do lose some students on question three.
- Practice Worksheet - You will need to estimate at times to find the equation of the graphs.
- Matching Worksheet - Students should find this to almost be an exercise in estimation because the questions are very diverse.
- Graphs Dealing with Sine and Cosine Five Pack of Worksheets - Determine the equations of the waves, since they are constant.
- Using a Calculator (Sin Cos and Tan) Worksheet Five Pack - Easy calculator work. Do it all together.

#### Homework Sheets

We used a slight blue tinted background to allow the graph to print well in all formats.

- Homework 1 - Each equation is graphed separately. I like to pick fixed values for x and then determine the value of y.
- Homework 2 - The graphs have a fixed frequency that is simple to detect.
- Homework 3 - On, the same set of axis from -10 to 10, graph y = -2sin (ℼ / 2*x) and y = -6cos(ℼ * x)

#### Practice Worksheets

Lots of graphs for you to make.

- Practice 1 - Try to see if the wave length fits on this problem.
- Practice 2 - Some of the waves are huge and others are short.
- Practice 3 - Don't go too big on these problems.