Is tan x even or odd?
Understand the Problem
The question is asking about the mathematical properties of the tangent function, specifically whether it is classified as even or odd. This involves understanding the definitions of even and odd functions and applying them to the tangent function.
Answer
tan(x) is an odd function.
The function tan(x) is an odd function.
Answer for screen readers
The function tan(x) is an odd function.
More Information
Tangent, represented as tan(x), satisfies the property f(-x) = -f(x), which is the definition of an odd function. This implies that tan(x) is symmetric with respect to the origin.
Tips
A common mistake is confusing the properties of even and odd functions. Remember, an odd function f(x) satisfies f(-x) = -f(x), while an even function satisfies f(-x) = f(x).
Sources
- AMSI Senior Years Mathematics - Trigonometric Functions - amsi.org.au
- Determine if Odd, Even, or Neither f(x)=tan(x) | Mathway - mathway.com
- Is the function f(x) = tan(x) odd, even, or neither? - Math Stack Exchange - math.stackexchange.com
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