Yes
Yes.
Yes. It is one of the trigonometric functions called ODD functions, wherein: f(-x) = - f(x) On the other hand, for EVEN functions, like the cosine function: f(-x) = f(x)
A sine wave is a periodic function and, by suitably adjusting the argument of the sine function, can be made to fit a wide functions with different frequencies.
It is to convert a function into a sum of sine (or cosine) functions so as to simplify its analysis.
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.
Yes
Yes.
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.
Yes. It is one of the trigonometric functions called ODD functions, wherein: f(-x) = - f(x) On the other hand, for EVEN functions, like the cosine function: f(-x) = f(x)
A sine wave is a periodic function and, by suitably adjusting the argument of the sine function, can be made to fit a wide functions with different frequencies.
An arcsine is any of the single- or multivalued functions which are inverses of the sine function.
It is to convert a function into a sum of sine (or cosine) functions so as to simplify its analysis.
The negative sine graph and the positive sine graph have opposite signs: when one is negative, the other is positive - by exactly the same amount. The sine function is said to be an odd function. The two graphs for cosine are the same. The cosine function is said to be even.
The basic primitive functions are constant function, power function, exponential function, logarithmic function, trigonometric functions (sine, cosine, tangent, etc.), and inverse trigonometric functions (arcsine, arccosine, arctangent, etc.).
An even function is symmetric about the y-axis. An odd function is anti-symmetric.
An even function is a function that creates symmetry across the y-axis. An odd function is a function that creates origin symmetry.