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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 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.
Is signum function an odd or even function?
both
Is it true or false that the cosine function is an odd function?
False; the cosine function is an even function as cos(-x) = -cos(x).
How do you determine if a function is even?
A function f(x) is Even, if f(x) = f(-x) Odd, if f(x) = -f(-x)
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 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.
What is the difference of odd and even functions?
An even function is symmetric about the y-axis. An odd function is anti-symmetric.
Is signum function an odd or even function?
both
Is the sine functions an odd function?
Yes. Along with the tangent function, sine is an odd function. Cosine, however, is an even function.
Is there a function that is both even and odd?
Yes f(x)=0 is both even and odd
Can a function be odd and even?
An even number can be divided by 2 evenly. An odd number will have a remainder of 1 when divided by 2. A function can be either.
What is the composition of an even and an odd function?
For an even function, f(-x) = f(x) for all x. For an odd function, f(-x) = -f(x) for all x.
Is A function with a graph that is symmetric about the origin an even function?
An even function is symmetric about the y-axis. If a function is symmetric about the origin, it is odd.
How do you determine if a function is even or odd?
You can tell if a function is even or odd by looking at its graph. If a function has rotational symmetry about the origin (meaning it can be rotated 180 degrees about the origin and remain the same function) it is an odd function. f(-x)=-f(x) An example of an odd function is the parent sine function: y=sinx If a function has symmetry about the y-axis (meaning it can be reflected across the y-axis to produce the same image) it is an even function. f(x)=f(-x) An example of an even function is the parent quadratic function: y=x2
How do you tell if a function is even or odd?
You can tell if a function is even or odd by looking at its graph. If a function has rotational symmetry about the origin (meaning it can be rotated 180 degrees about the origin and remain the same function) it is an odd function. f(-x)=-f(x) An example of an odd function is the parent sine function: y=sinx If a function has symmetry about the y-axis (meaning it can be reflected across the y-axis to produce the same image) it is an even function. f(x)=f(-x) An example of an even function is the parent quadratic function: y=x2
Is f of x equal to negative x an even or odd function?
It is an odd function. Even functions use the y-axis like a mirror, and odd functions have half-circle rotational symmetry.
