## Reflection: Connection to Prior Knowledge Writing Sinusoidal Models - Section 1: Bell work

We use the general equation y=a sin b(x-c)+d. Students need to determine the parameters a, b, c and d. Some books use a different version of the general equation but I decided to use this one to help students connect to other functions. I have used y=a sin (bx-c)+d. This is the equation my book uses I find this equation more difficult for the students to use when writing models. It seems to be easier for students to take an equation like y=3sin(2x-pi)+1 and rewrite it to y=3sin2(x-pi/2)+1 and determine the key features. As students become more proficient with the trigonometric functions they will see how to use the first equation.

I know that some students will struggle with determining how to use the period to find "b". When we do this problems the students will share their processes in determining each parameter. I also refer back Graphing Trigonometric Functions Day 3 to remind students about the relationship between the period and the parameter "b".

Another common error is correctly writing the (x-c) portion of the general solution incorrectly. This was also a problem when we worked with conics. Some students do not look at the structure of the equation and see we are subtracting not adding. Once I remind students how we wrote equations for conics students remember what to do.

I find it very important to connect as many processes we do with trigonometric functions to other functions. I feel that many students struggle with trigonometric functions because they see the functions as some strange function that is completely different than other functions. The functions do have some unique characteristics but transformations work the same.

Common Errors
Connection to Prior Knowledge: Common Errors

# Writing Sinusoidal Models

Unit 8: Graphing Trigonometric Functions
Lesson 9 of 13

## Big Idea: How can trigonometric functions be used to predict the weather and the sunrise?

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65 minutes

### Katharine Sparks

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