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.