# Is the cosine function an odd function?

- No. Cosine, along with sec, is an even function. The odd functions are sin, tan, csc, and cot. The reason for this is because is you take the opposite of the y-value for the cosine function, the overall value of the function is not affected.
- Take, for example, cos(60 degrees), which equals POSITIVE 1/2.
- If you flip it over the x-axis, making the y's negative, it becomes cos(-60 degrees), or cos(300 degrees). This equals POSITIVE 1/2.
- Now let's look at an odd function. For example, sin(30 degrees) equals POSITIVE 1/2. Now take the opposite of this.
- sin(-30 degrees), or sin(330 degrees), equals NEGATIVE 1/2. This is because it is found in the fourth quadrant, where the y's are negative. Sine of theta, by definition, is y divided by r. If y is negative, sine is negative.

No.

### 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… Read More

### Is it true or false that the cosine function is an odd function?

False; the cosine function is an even function as cos(-x) = -cos(x).

### Is the sine functions an odd function?

Yes. Along with the tangent function, sine is an odd function. Cosine, however, is an even function.

### What is the difference between negative sine and cosine graphs and positive sine and cosine graphs?

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.

### What is even and odd wave function?

A basic wave function is a sine or cosine function whose amplitude may have a value other than 1. The cosine function is an even function because it is symmetrical about the y-axis. That is, f(-x) = f(x) for all x. The sine function is an odd function because it is antisymmetrical about the y-axis. That is, f(-x) = -f(x) for all x.

### When do you use even odd and neither functions?

You use an even function if f(-x) = f(x) for all x.You use an odd function if f(-x) = -f(x) for all x. and you use neither if there is at least one point for which one or the other of the above is not true. Most functions are neither even nor odd.

### What are the Differentiate the sine wave and cosine wave?

The differential of the sine function is the cosine function while the differential of the cosine function is the negative of the sine function.

### Is a cosine function continuous?

Yes. The cosine function is continuous. The sine function is also continuous. The tangent function, however, is not continuous.

### What is the formula for the y-intercept of a cosine function?

The Y-Intercept of the cosine function is X = 0, Y = cosine(0) = 1.

### How do you get a period of 3 in a cosine function?

The argument of the cosine function must be (2pi/3)*x radians

### What is the rage of a cosine function?

I was not aware that the cosine function was in fashion! The range, on the other hand, is [-1, 1].

### What is the derivation of the wave function?

A simple wave function can be expressed as a trigonometric function of either sine or cosine. lamba = A sine(a+bt) or lamba = A cosine(a+bt) where lamba = the y value of the wave A= magnitude of the wave a= phase angle b= frequency. the derivative of sine is cosine and the derivative of cosine is -sine so the derivative of a sine wave function would be y'=Ab cosine(a+bt) """"""""""""""""""" cosine wave function would be… Read More

### What is the inverse of the cosine function?

The inverse of the cosine function is arcosine. The domain is −1 ≤ x ≤ 1 since the range of the cosine function is from -1 to 1. The range is from 0 to pi radians or 0 to 180 degrees.

### What are the zeros in sine and cosine function?

A "zero of a function" is a point where the dependent value (usually, Y) is zero. In the function f(x) = x2 - 2, for example, there are zeroes at -1.414 and +1.414. The zeroes of the sine function are at all integer multiples of pi, i.e. 0, pi, 2pi, 3pi, etc. The zeroes of the cosine function are at the same points plus pi/2, i.e. pi/2, 3pi/2, 5pi/2, etc. Another way to look at… Read More

### How does the tangent function relate to sine and cosine?

Tangent = sine/cosine provided that cosine is non-zero. When cosine is 0, then tangent is undefined.

### Which ratios correctly describes the cosine function?

The cosine function on a right triangle is Adjacent leg divided by the hypotenuse of the triangle.

### Why is cos an even function?

Cosine is an even function because : cos ( theta ) = cos ( -theta) <---------------------[ Answer ]-------------

### How can you tell if a graph is a sine function or a cosine function?

sine graph will be formed at origine of graph and cosine graph is find on y-axise

### Is tangent sine divided by cosine?

Yes, except at odd multiples of pi/2 radians, where the cosine is zero so that the division is not defined.

### What are the domains of sine cosine and tangent?

The domain of a function is the set of values of the independent variable for which the function is valid. In practice, this is the allowable values of X or, in this case, theta. The sine and cosine functions have a domain of all numbers from negative infinity to positive infinity. The tangent function, however, is sine(theta) / cosine(theta). Cosine(theta) has value of zero at theta equal to pi / 2, 3pi/2, 5pi/2, ... in… Read More

### What makes cosine equal 0?

Cosine is a periodic function which is continuous and oscillates between +1 and -1. Therefore, from time to time, it must be 0. cos(x) = 0 whenever x = k*pi/2 for all odd integer values of k (pi/2, 3pi/2, 5pi/2 and so on).

### Is x the cosine in math?

No, actually x is the variable in mathematics. cos(x) or cosine is considered a trigonometric function with a variable x.

### What is the graphic representation of cosine function?

Just like the sine function displaced by pi/2. In other words the cosine equals 1 at 0 degrees, 0 at 90 degrees, -1 at 180 and so on.

### What is a function of fourier analysis?

It is to convert a function into a sum of sine (or cosine) functions so as to simplify its analysis.

### Is sine-30 equal to -sine30?

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)

### How do you convert a sine curve function to a cosine curve function?

One way is to shift it to the left by a quarter of the period.

### What are even and odd functions?

An even function is a function that creates symmetry across the y-axis. An odd function is a function that creates origin symmetry.

### Is signam function even or odd and why?

I have no idea about the signam function. The signum function is odd because sgn(-x) = -sgn(x).

### How do you differentiate a cosine function That is what is the derivative of the cosine of x with respect to the independent variable x?

The derivative of cosine of x is simply the negative sine of x. In mathematical terms f'(x) = d/dx[cos(x)] = -sin(x)

### What are the attributes of a cosine function?

There are many "attributes" of a cosine function. Some examples of attributes are as follows: For, constants a, b, n, y=a*cos(nx)+b has an amplitude of a, a period of 2pi/n, a range of [-a+b,a+b], a derivative of y'=-an*sin(nx).

### Properties of cosine and sine function?

The properties of the cosine and sine function are based on the X and Y coordinates of a point on a circle that has a radius of 1 and a center at the origin (X=0,Y=0). If the angle of the line from the origin to the edge of the circle, at any arbitrary point (X,Y), with respect to the X axis is theta, then sine(theta) is X, and cosine(theta) is Y.

### 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 cos negative results positive?

It doesn't really. Depending on the exact value of the argument, the cosine function can give both positive and negative results, for a negative argument. As to "why" the sine, or cosine, functions have certain values, just look at the function definition. Take points on a unit circle. The sine represents the y-coordinate for any point on the circle, while the cosine represents the x-coordinate for such a point. (There are also other ways to… Read More

### What is the trigonometric function sec?

The function sec(x) is the secant function. It is related to the other functions by the expression 1/cos(x). It is not the inverse cosine or arccosine, it is one over the cosine function. Ex. cos(pi/4)= sqrt(2)/2 therefore secant is sec(pi/4)= 1/sqrt(2)/2 or 2/sqrt(2).

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

You can tell if a function is even or odd by looking at its graph. If a function has rotational symmetry about the origin (meaning it can be rotated 180 degrees about the origin and remain the same function) it is an odd function. f(-x)=-f(x) An example of an odd function is the parent sine function: y=sinx If a function has symmetry about the y-axis (meaning it can be reflected across the y-axis to produce… Read More

### How do you tell if a function is even or odd?

You can tell if a function is even or odd by looking at its graph. If a function has rotational symmetry about the origin (meaning it can be rotated 180 degrees about the origin and remain the same function) it is an odd function. f(-x)=-f(x) An example of an odd function is the parent sine function: y=sinx If a function has symmetry about the y-axis (meaning it can be reflected across the y-axis to produce… Read More

### How are ratios for sin and cosine alike?

sin(x) = cos(pi/2 - x). Thus sine is simply a horizontal translation of the cosine function. NB: angles are measured in radians.

### Why we use sin cos etc in sinusoidal wave?

By its very mane, a sinusoidal wave refers to a sine function. The cosine function is simply the sine function that is phase-shifted.

### What is the six trigo function of acute angle?

Sine, Cosine, Tangent, Cosecant, Secant, Cotangent.

### What is trigonometry's circular function?

The basic circular functions are sine, cosine and tangent. Then there are their reciprocals and inverses.

### Cos x equals -cos x plus 1?

No, but cos(-x) = cos(x), because the cosine function is an even function.