Determining Whether a Trig Function is Odd, Even, or Neither

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We've explored trigonometric functions in the past, but today's video is a bit different. While we can easily determine if a function is odd or even by looking at its graph, Professor Edward Burger also shows how to look at the function to come to the same conclusion.

A function is even if it's symmetric about the Y-axis, so anything done on the right side is mirrored on the left side. In math terms even would be if f(-x) = f(x). A function is odd if it has some symmetry but it's more like a flip-of-a-mirror symmetry. Whatever is done on the right, the same thing is done on the left but sort of in reverse. This can be also be explained in math terms as f(-x) = -f(x).

In today's free Pre-Calculus lecture, you'll learn how to visually determine whether a trigonometric function is odd, even, or neither. It really helps to see the graphs to understand this concept. You'll learn that sine is odd, cosine is even and tangent is odd and how to prove this with both the graph and the function itself. Don't forget that trigonometric functions can also be neither odd nor even if it's not symmetric to either the Y-axis or to the origin. This is one lecture you'll want to see as the visuals really help explain and show the difference between odd and even functions.


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This page contains a single entry by April Stockwell published on March 3, 2011 2:30 PM.

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