# Is the graph of sin odd or even?

## Is the graph of sin odd or even?

Sine is an odd function, and cosine is an even function.

**Why is sin an odd function?**

E.G. If f(−x)≠f(x)orf(−x)≠−f(x) the function is not even or odd. Now the answer you need: the function y=sinx is odd, because sin(−x)=−sinx.

**Is sin2x even or odd?**

1 Answer. sin 2x is an odd function.

### How do you determine whether a function is even or odd?

If you end up with the exact same function that you started with (that is, if f (−x) = f (x), so all of the signs are the same), then the function is even; if you end up with the exact opposite of what you started with (that is, if f (−x) = −f (x), so all of the signs are switched), then the function is odd.

**Is the sine function symmetric?**

The trigonometric functions cosine, sine, and tangent satisfy several properties of symmetry that are useful for understanding and evaluating these functions.

**Why is sin2x an odd function?**

Since sin(−2x) sin ( – 2 x ) ≠ ≠ sin(2x) sin ( 2 x ) , the function is not even. A function is odd if f(−x)=−f(x) f ( – x ) = – f ( x ) . Multiply −1 – 1 by sin(2x) sin ( 2 x ) .

## What is an odd function graph?

A function is odd if −f(x) = f(−x), for all x. The graph of an odd function will be symmetrical about the origin. For example, f(x) = x3 is odd. That is, the function on one side of x-axis is sign inverted with respect to the other side or graphically, symmetric about the origin.

**Which of the following is an odd function?**

Example: x and sinx are odd functions. A function f(x) is an even function if f(-x) = f(x). Thus g(x) = x2 is an even function as g(x) = g(-x). So the function g(x) = 4x is an odd function.

**How do you prove that cos is an even function?**

Explanation: cos(x)=cos(−x) , therefore cosine is an even function. Alvin L. To prove that cos(θ) is even, i.e. that cos(−θ)=cos(θ) , we can use the unit circle, which mind you, is the definition of cosine arguments outside the interval [0,π2] .

### Can a sine be negative?

As the angle increases from 180° to 270°, the sine increases in magnitude but is now negative, so, the sine decreases from 0 to -1. As the angle increases from 180° to 270°, the cosine decreases in magnitude but is now negative, so, the cosine increases from its minimum of -1 to a value of 0.