## Reflection: Developing a Conceptual Understanding Sine and Cosine Day 1 of 2 - Section 2: Finding Sine and Cosine on Circles in the Coordinate Plane

Most trigonometry books have students using the unit circle to find trigonometric values and then transfer to all real numbers. When I used this sequence, I found that students struggled and made mistakes in finding the trigonometric values when given a point such as (3,4). Student would not find the value of 4 since they had in their mind that sin t=y and cos t=x. Once I change to to all real numbers and all points in the plane first the students had less confusion about how to find sine and cosine.

The original activity worked with the unit circle and this still confused students. Again once I changed the activity to be more general my students had less confusion. As we move on in the unit we do the unit circle. The students now do not just think the sin t=y but will always say sin t= y/r and on the unit circle the r=1 so sin t=y.

I also feel that doing the activity in this format helps students understand why reference angles can be used to find the trigonometric values of an angle greater than 90 degrees. Students see how the point on the terminal side give the values for the legs of the triangle.

As we know Common Core asks us to help students develop a deeper understanding of mathematical ideas and I find that today's activity helps my students understand at a deeper level.

Why not the Unit Circle First
Developing a Conceptual Understanding: Why not the Unit Circle First

# Sine and Cosine Day 1 of 2

Unit 7: Trigonometry as a Real-Valued Functions
Lesson 5 of 13

## Big Idea: Students explore angles on a circle and measure values for the x and y coordinate to develop a method for evaluating trigonometric functions using the coordinate plane.

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43 minutes

### Katharine Sparks

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