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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.
If you add 3 to an even number the sum would be odd or even?
Odd. Even + Even = Even Odd + Odd = Even Odd + Even = Even + Odd = Odd
Does multiplying an odd number by an even number give an even answer?
odd * odd = odd answer even * even = even answer odd * even = even answer
When you add to even numbers is the answer always even?
Yes. Even + Even = Even, Odd + Odd = Even and Even + Odd or Odd + Even = Odd
What is even times even equal?
even times even = even odd times odd = odd even times odd = even
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.
Can a function be both even and odd functions?
yes
What is the difference of odd and even functions?
An even function is symmetric about the y-axis. An odd function is anti-symmetric.
Why are functions called odd or even?
Probably because polynomials and convergent power series in which all terms have even degree are even functions, and similarly for odd.
When do you use even odd and neither functions?
Basically, a knowledge of even and odd functions can simplify certain calculations. One place where they frequently appear is when using trigonometric functions - for example, the sine function is odd, while the cosine function is even.
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 the sine functions an odd function?
Yes. Along with the tangent function, sine is an odd function. Cosine, however, is an even function.
If you add 3 to an even number the sum would be odd or even?
Odd. Even + Even = Even Odd + Odd = Even Odd + Even = Even + Odd = Odd
Does multiplying an odd number by an even number give an even answer?
odd * odd = odd answer even * even = even answer odd * even = even answer
Is even times even odd?
even times even = even odd times even = even odd times odd = odd
Can properties of a function be discovered from its Maclaurin series Give examples.?
Best example is that an "odd" (or "even") function's Maclaurin series only has terms with odd (or even) powers. cos(x) and sin(x) are examples of odd and even functions with easy to calculate Maclaurin series.
When you add to even numbers is the answer always even?
Yes. Even + Even = Even, Odd + Odd = Even and Even + Odd or Odd + Even = Odd
