Practice Symmetry (Meta) in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

A property of a mathematical object that remains unchanged under a specified transformation — reflection, rotation, translation, or algebraic substitution.

Looks the same from different perspectives or after certain changes.

Example 1

easy
Show that the equation x^2 + y^2 = 25 is symmetric about both coordinate axes and the origin. Verify by substituting (x,y) = (3,4) and its reflections.

Example 2

medium
Use symmetry to evaluate \displaystyle\sum_{k=0}^{n} \binom{n}{k}(-1)^k for even n=4.

Example 3

easy
Determine whether f(x) = x^3 is odd, even, or neither, by testing the symmetry condition.

Example 4

medium
Use the symmetry of \sin (odd function) and \cos (even function) to simplify: \sin(-\theta) + \cos(-\theta).
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