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How do you determine if a relation is a function?
A relation is a function if every input has a distinct output.
What are even and odd functions?
An even function is a function that creates symmetry across the y-axis. An odd function is a function that creates origin symmetry.
Why is cos an even function?
An even function is one where f(x) = f(-x) For cosine, cos(x) = cos(-x), thus cosine is an even function.
Is signum function an odd or even function?
both
Why is the secant function is an even function and the tangent and cosecant are odd functions?
I find it convenient to express other trigonometric functions in terms of sine and cosine - that tends to simplify things. The secant function is even because it is the reciprocal of the cosine function, which is even. The tangent function is the sine divided by the cosine - an odd function divided by an even function. Therefore it is odd. The cosecant is the reciprocal of an odd function, so it is naturally also an odd function.
