# Graphs Dealing with Sine and Cosine Problems

These worksheets and lessons help students learn how to read and interpret graphs that include the sine and cosine functions. While this may not be every studentâ€™s favorite topic to study, the applications of it produce some amazing breakthroughs that help us better understand the world around us through math. I would encourage teachers to always share the applications of these functions in the real world with students. It will definitely leave them feeling more drawn to material. It should help motivate them to the next level.

### Aligned Standard: HSG-SRT.D.10

- 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.

- Answer Keys - These are for all the unlocked materials above.

### 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.

### Math Skill Quizzes

We start to ask you for the equation of the graph.

- Quiz 1 - Determine the equation for graph.
- Quiz 2 - Start by picking two points and finding where x is a fixed whole number.
- Quiz 3 - The y-intercept is easy. At what value of y (point) does it hit the y-axis?

### What Are the Characteristics of Graphs of Sine and Cosine Functions?

We can use these functions to model a number of different phenomena like sound and light. There are a ton of different applications for these functions, the most interesting one that I heard of lately is creating predictive weather modelling. A series of climate scientists have built an algorithm that simply is feed data from 9 different weather stations, and it predicts the weather for the next 5 days with 87% accuracy. That 13% of inaccuracy is due to the limitations of the equipment that is monitoring the conditions of nature. The model works by reflecting a graph of these functions.

The sine and cosine function relate numeric values to points of the unit circle. With this in mind, we can imagine what those values would look like when they are plotted on the cartesian plane. If you were to consider the sine function, the x variable is the input value for the function while still maintaining a horizontal position on the angle. The y variable would be the output of the function and represent the vertical position on the angle. We can then take these values and plot them in a continuous manner to visualize this function. You can do the same thing with cosine function.

Because of the manner in which functions relate to the unit circle, they do often give off distinct shapes when they are plotted on a graph. They will often form waves in horizontal direction. They characteristically look like a snake moving up and down. We often will make sense of these waves by measuring the distance between each wave and the height or descent of the individual waves. The height is commonly referred to as the amplitude. The greater the value, the taller the wave. The graphs that they form are reflective and often continuous.