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## Symmetry of the Unit Circle and Odd-Even Properties

#### High School - HSF-TF.A.4

What are the Odd-Even Properties of Trigonometric Functions? Did you know that even the trigonometric functions can be categorized in odd and even functions? Well, like all other functions and numbers, even these functions fall into the categories of even, odd, and or neither. Even functions satisfy the following condition; f(x)=f(-x) Odd functions satisfy the following condition; f(x)=-f(-x) In trigonometric functions, non-polynomial functions, cosine functions are even, while the sine and tangent functions are odd functions. The even-odd properties help in solving trigonometric functions when the variable within the function is negative. These properties are given by; cos ⁡ -β = cos⁡β, sin⁡ -β = -sin⁡β, tan⁡ -β = -tan⁡ β , csc⁡ -β = -csc⁡β, sec⁡ -β = sec⁡β, cot⁡ -β = -cot ⁡β 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.

### Printable Worksheets And Lessons  #### Homework Sheets

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.

#### Practice Worksheets

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.