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What does it mean when a graph is odd?

What does it mean when a graph is odd? A function f(x) is odd when f(-x)=-f(x) for every x. The graph of an odd function has a particular rotational symmetry, so the graph will look the same after you rotate it 180º about the origin.

Is sine an odd function?

Sine is an odd function, and cosine is an even function. … A function f is said to be an even function if for any number x, f(–x) = f(x). Most functions are neither odd nor even functions, but some of the most important functions are one or the other.

Are numbers odd?

The odd numbers from 1 to 100 are: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99.

What does it mean for a function to be even odd or neither?

If we get an expression that is equivalent to f(x), we have an even function; if we get an expression that is equivalent to -f(x), we have an odd function; and if neither happens, it is neither!

What does a sine curve look like?

To graph the sine function, we mark the angle along the horizontal x axis, and for each angle, we put the sine of that angle on the vertical y-axis. The result, as seen above, is a smooth curve that varies from +1 to -1. Curves that follow this shape are called ‘sinusoidal’ after the name of the sine function.


Is CSC odd or even?

Cosine and secant are even; sine, tangent, cosecant, and cotangent are odd.

What is an odd function times an odd function?

An even function times an odd function is odd, and the product of two odd functions is even while the sum or difference of two nonzero functions is odd if and only if each summand function is odd. The product and quotient of two odd functions is an even function.

Is 0 an odd or an even number?

So what is it – odd, even or neither? For mathematicians the answer is easy: zero is an even number. … Because any number that can be divided by two to create another whole number is even.

Is 3 an odd or even number?

All the numbers ending with 1,3,5,7 and 9 are odd numbers. … All the numbers ending with 0,2,4,6 and 8 are even numbers. For example, numbers such as 14, 26, 32, 40 and 88 are even numbers.

Can 3 odd numbers make an even number?

Without cheating, it’s not possible because sum of three odd numbers can’t be even.

What is odd and even number?

An even number is a number that can be divided into two equal groups. An odd number is a number that cannot be divided into two equal groups. Even numbers end in 2, 4, 6, 8 and 0 regardless of how many digits they have (we know the number 5,917,624 is even because it ends in a 4!). Odd numbers end in 1, 3, 5, 7, 9.

Is Xsinx an even function?

Even functions are symmetrical about the y-axis. Odd functions have symmetry about the origin. thus xsinx is an even function.

How do you tell if a graph is a function?

Inspect the graph to see if any vertical line drawn would intersect the curve more than once. If there is any such line, the graph does not represent a function. If no vertical line can intersect the curve more than once, the graph does represent a function.

How can you tell the difference between a sine and cosine graph?

In a cosine graph, a positive or negative number vertically flips the graph and determines whether the graph starts at the maximum (if it’s positive) or minimum (if it’s negative). For a sine graph, a positive or negative number vertically flips the graph like it does with a cosine graph.

What are the three characteristics of a sine wave?

Sinusoidal Amplitude, Frequency, and Phase

The three characteristics that separate one sinusoid from another are amplitude, frequency, and phase.

Where does a sine wave start?

The Sine Function has this beautiful up-down curve (which repeats every 2π radians, or 360°). It starts at 0, heads up to 1 by π/2 radians (90°) and then heads down to −1.

How do you go from sin to CSC?

The secant of x is 1 divided by the cosine of x: sec x = 1 cos x , and the cosecant of x is defined to be 1 divided by the sine of x: csc x = 1 sin x .

Is Tan an odd or even function?

Because sine, cosine, and tangent are functions (trig functions), they can be defined as even or odd functions as well. Sine and tangent are both odd functions, and cosine is an even function. In other words, … tan(–x) = –tan x.

Why is a function neither even nor odd?

Note: A function can be neither even nor odd if it does not exhibit either symmetry. For example, f(x)=2x f ( x ) = 2 x is neither even nor odd. Also, the only function that is both even and odd is the constant function f(x)=0 f ( x ) = 0 .

What happens when you integrate an odd function?

Integrating Even and Odd Functions

An odd function is one in which f(−x)=−f(x) for all x in the domain, and the graph of the function is symmetric about the origin. … Integrals of odd functions, when the limits of integration are similarly [−a,a], evaluate to zero because the areas above and below the x-axis are equal.

Is the number 1 even?

Every integer is either of the form (2 × ▢) + 0 or (2 × ▢) + 1; the former numbers are even and the latter are odd. For example, 1 is odd because 1 = (2 × 0) + 1, and 0 is even because 0 = (2 × 0) + 0.

Is Infinity odd or even?

I explained that infinity is neither even nor odd. It’s not a number in the usual sense, and it doesn’t obey the rules of arithmetic. All sorts of contradictions would follow if it did. For instance, “if infinity were odd, 2 times infinity would be even.

Is 0 a real number?

Real numbers can be positive or negative, and include the number zero. They are called real numbers because they are not imaginary, which is a different system of numbers.

Is 3 an evil number?

Examples. The first evil numbers are: 0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39 …

Is 3.5 odd or even?

Is 3.5 odd or even? The definition of an even number is one that, when divided by 2, forms an integer with no remainder. For example: 7 / 2 = 3 and 1 remainder, or 3.5, which is not an integer and therefore 7 must be odd. 3.2 / 2 = 1.6 which is not an integer and therefore 3.2 is an odd number.

Is six an even number?

Even numbers are those numbers that can be divided into two equal groups or pairs and are exactly divisible by 2. For example, 2, 4, 6, 8, 10 and so on.

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