Reflections and Graphs of Trigonometric Functions

In Lesson 5-5, part a we will be studying reflections and even and odd functions.

In Lesson 5-5, part b, you will learn about the basic shapes of sine, cosine, tangent, cosecant, secant and cotangent graphs.

In the next lesson (5-6) we will look at the graphs of sine and cosine in more depth and learn about their many applications in math, music, physics, signal processing, electrical engineering, and counterfeiting, to name a few.

Reflections Across a Line or a Point

• Given the coordinates of a point on the unit circle, find its reflections across the x-axis, the y-axis, and the origin

To reflect a point across a line:

1. Determine the distance between the line and the point
2. Draw a point that is the same distance away, but on the other side of the line
3. Reflect in a direction perpendicular to the line

Example

In the diagram to the left, the reflection of the point (3/5, 4/5) across the y-axis is (-3/5, 4/5). Notice that the reflected point was placed the same distance from the y-axis in the direction perpendicular to the y-axis.   The reflection of (3/5, 4/5) across the x-axis is (3/5, -4/5).   The reflection of (3/5, 4/5) across the origin (0, 0) is (-3/5, -4/5). Notice on this last one that you are reflecting across a point, rather than a line.

 

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