Even and Odd Trig Functions Worksheets
Being able to classify a trig function as even, odd, or neither has a great many uses that you could put to work for yourself. Not only do these properties and identities help in simplifying trigonometric functions, but they help in proving and solving complex trigonometric problems. This series of worksheets and lessons have students learn how to judge the symmetry of trig. functions and classify them. For their we put them to a wide variety of uses.
Aligned Standard: HSF-TF.A.4
- Warm-up Step-by-step Lesson - I know this does not hit the skill exactly, but it works students through the basic procedure needed for the guided lesson.
- Guided Lesson - You can classify the odd-even-neutral quality when you finalize the calculation.
- Guided Lesson Explanation - These all work out in straight line ups.
- Practice Worksheet - We are working with a whole bunch of different trig functions here.
- Matching Worksheet - Find the matching outcomes here. The unit circle comes in handy.
- Answer Keys - These are for all the unlocked materials above.
This section is all about comparing values.
- Homework 1 - The sine function f(t) = sin t is odd and the cosine function g(t) = cos t is even; that is, for every real number t.
- Homework 2 - Note that the signs of the answers are consistent with the fact that the terminal side of the angle lies in quadrant I.
- Homework 3 - Connect the dots and find where these values lie.
I find that many advanced students just memorize all of the possibilities. I think it's more important to understand it, than to memorize it.
- Practice 1 - When ever two angle expressions are symmetric on a unit circle you can easily pick out reference angles.
- Practice 2 - Because the unit circle is symmetric it can be used to learn a great deal about a system.
- Practice 3 - This type of math is often used to construct geometric figures.
Math Skill Quizzes
It's all about Π sliced tons of different ways.
- Quiz 1 - Three dimensional objects can be modelled using this method.
- Quiz 2 - A consistent model can be reshaped using points that exist with it.
- Quiz 3 - This is one of the more complex quizzes.
Odd, Even, and Neither Properties of Trigonometric Functions
There are times where you will be simplifying an expression when you can be quite certain that the variable inside is negative. Under those circumstances it is helpful to understand the nature of the function. Did you know that trigonometric functions can be categorized as odd, even, or neither?
Even functions satisfy the following condition: f(x)=f(-x) and is symmetric with y-axis.
Odd functions satisfy the following condition: -f(x)=-f(-x) and is symmetric with respect to the origin.
In trigonometric functions, non-polynomial, cosine, and secant functions are classified as even. While the sine, cosecant, tangent, and cotangent are classified as odd functions. The even-odd properties help in solving trigonometric functions when the variable within the function is negative.
Once you are able to classify a function there are some general rules that apply to make your life simpler. If you are calculating the sum or product of functions that are both odd or both even, their sum stays with that classification. If you are finding a sum between an even and odd functions, the sum with be classified as neither. If you are calculating the product of even and odd function the product will be odd.