## Reflection: Grappling with Complexity Trigonometric Graphs (Day 1 of 3) - Section 1: Bell work

Many students struggle with the difference in using the unit circle to evaluate a trigonometric function and graphing the trigonometric functions. If I use y=sinx instead of f(t)=sin t, this struggle is really a problem.

I think some of the issue is that the unit circle is working with three different variables, the (x,y) coordinate and the angle theta. I know when I first started teaching I did not think about the structure of the unit circle. I also did not consider the idea that the x and y of the unit circle are the outputs for the trigonometric functions. After working with students who struggle. I began to develop some techniques to help students separate the two concepts.

When I begin teaching graphing of the trigonometric functions I remind students how we graph other functions. I discuss how the x is the input and the y is the result or output.  When I will also write functions using different variables such and f(t)=t^3. We label the axis and discuss what is the independent and dependent variable.

Once I move to the trigonometric functions I wait to write the function in terms of x and y. I will use t or theta for the angle. I also make sure we label the axis of the graphs to help students connect with x and y. As the students work some will say can I use x and y instead of t and f(t). I will question students about changing the variables. When we are graphing functions not in context I will allow the variables to be altered.

After a couple of days of graphing I will change the variables to x and y. At this point most students have become work with the trigonometric graphs long enough not to confuse the x and y in the equation with the x and y of the unit circle.

Confusion between unit circle and graphing functions
Grappling with Complexity: Confusion between unit circle and graphing functions

# Trigonometric Graphs (Day 1 of 3)

Unit 8: Graphing Trigonometric Functions
Lesson 1 of 13

## Big Idea: By using technology to graph the functions, students identify the domain and range of the 6 trigonometric functions.

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35 minutes

### Katharine Sparks

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