# What is the domain of sin and cos?

## What is the domain of sin and cos?

all real numbers
The domain of the sine and cosine functions is all real numbers. The range of both the sine and cosine functions is [−1,1]. The sine and cosine of an angle have the same absolute value as the sine and cosine of its reference angle.

What is domain of Sine?

In the sine function, the domain is all real numbers and the range is -1 to 1. Here is the graph of the cosine function: This has the same domain and range as the last graph. Again, the domain is all real numbers, and the range is -1 to 1.

What is the restricted domain for cosine?

The restriction that is placed on the domain values of the cosine function is 0 ≤ x ≤ π (see Figure 2 ). This restricted function is called Cosine.

### What is domain of Sinx?

The graph of y=sin(x) is like a wave that forever oscillates between -1 and 1, in a shape that repeats itself every 2π units. Specifically, this means that the domain of sin(x) is all real numbers, and the range is [-1,1].

What is the domain of Arctan?

Domain and range: The domain of the arctangent function is all real numbers and the range is from −π/2 to π/2 radians exclusive (or from −90° to 90°). The arctangent function can be extended to the complex numbers, in which case the domain is all complex numbers.

What is the domain of Arcsin?

Additionally, the domain of arcsin x = range of sin x = [−1, 1] and range of arcsin x = domain of sin x = [− π 2 , π 2 ]. Note: arcsin(x) is the angle in [− π 2 , π 2 ] whose sine is x.

#### Is SEC the inverse of cos?

The secant ( sec ⁡ ) (\sec) (sec) The secant is the reciprocal of the cosine. It is the ratio of the hypotenuse to the side adjacent to a given angle in a right triangle.

What is the domain for Arcsin?

Is arctan undefined?

If x=0 then arctanyx is undefined, but you may be able to find a limit as x approaches 0. When converting from rectangular to cylindrical, the statement that θ=arctanyx is a bit sloppy. You need to start with if x=0,θ=±π2 depending on the sign of y because the arctangent never returns ±π2.

## What’s the domain of arctan?

How is the sine related to the cosine?

The relationship between the cosine and sine graphs is that the cosine is the same as the sine – only it’s shifted to the left by 90 degrees, or π /2. The trigonometry equation that represents this relationship is Look at the graphs of the sine and cosine functions on the same coordinate axes, as shown in the following figure.

What is the difference between sine and cosecant?

is that cosecant is (trigonometry) in a right triangle, the reciprocal of the sine of an angle symbols: cosec, csc while sine is (trigonometry|mathematics) in a right triangle, the ratio of the length of the side opposite an angle to the length of the hypotenuse. cosecant. English. Noun.

### Is the domain all real numbers?

Domain: The set of all possible input values (commonly the “x” variable), which produce a valid output from a particular function. It is the set of all values for which a function is mathematically defined. It is quite common for the domain to be the set of all real numbers since many mathematical functions can accept any input.

What is the domain and range of a sine function?

The sine and cosine functions have a period of 2π radians and the tangent function has a period of π radians. Domain and range: From the graphs above we see that for both the sine and cosine functions the domain is all real numbers and the range is all reals from −1 to +1 inclusive.