Domain And Range Of A Trig Function

The outputs of the trig functions are real numbers.

Domain and range of a trig function. 2 sin 3x 0. You can t put just any angle into some of the functions. All real numbers period pi x intercepts. 1 y 1 period 2π it is a odd function graph of sin x function more graphs on sine function for y f x 2 sin x and y f x 3 sin x we can see that range get increased in the similar way.

It is defined for all real values of x range. However its range is such at y r because the function takes on all values of y. So we will not the above situation at any more. Find the domain and range of y cos x 3.

All real numbers except pi 2 k pi k is an integer. F x tan x graph. Domain of sin x and cos x in any right angle triangle we can define the following six trigonometric ratios. In order to find the domain let us equate the denominator to 0.

Notice that the range is simply. That situation happens in a function such as h x 3x 2. In this case transformations will affect the domain but not the range. The range of a function consists of all its output values the numbers you get when you input numbers from the domain into the function and perform the function operations on them.

Since tan x tan x then tan x is an odd function and its graph is symmetric with respect the origin. Y 0 symmetry. 4 y 2 y r. To make the students to understand domain and range of a trigonometric function we have given a table which clearly says the domain and range of trigonometric functions.

X k pi where k is an integer. Sin 3x 2. This is impossible because the minimum value of sin is 1 and maximum value is 1. Sine and cosine are very cooperative and have the same domain and range.

So the domain is all real values. The hitch here is that the different trig functions have different domains and ranges. Sometimes a range can be all possible real numbers it has no limit. Graphically speaking the domain is the portion of the.

The range of a function is the list of all possible outputs y values of the function. Sine function y f x sin x domain. Range for sin function is between 1 and 1 1 sin 3x 1. Range of a trig function.