Which trigonometric function is an odd function and why?
Understand the Problem
The question is asking which trigonometric function is classified as an odd function, along with an explanation of the reason behind this classification.
Answer
Sine function
The final answer is that the sine function is an odd function because it satisfies the property f(-x) = -f(x), specifically sin(-x) = -sin(x) for all x.
Answer for screen readers
The final answer is that the sine function is an odd function because it satisfies the property f(-x) = -f(x), specifically sin(-x) = -sin(x) for all x.
More Information
The sine function is considered an odd function because it has rotational symmetry around the origin of a graph. This means that if you rotate the sine wave 180 degrees, it will look the same. This property is a direct result of the sine function’s mathematical definition.
Tips
Common mistakes include confusing the properties of sine with those of cosine, which is an even function and has different symmetry properties.
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