Graph Of Inverse Sine Math

Before reading this post you may wish to review graphs of basic trigonometric functions and introduction to inverse trigonometric functions.

Graph of inverse sine math. Here is cosine and inverse cosine plotted on the same graph. The fact remains that you can t learn math by standing on the sidelines. First graph y x. Inverse sine has a domain of 1 1 and a range of π 2 π 2.

Here s the graph of the inverse sine function y sin 1 x or y arcsin x. Cosine and inverse cosine. How to graph the sine. Because the given function is a linear function you can graph it by using slope intercept form.

You can now graph the function f x 3x 2 and its inverse without even knowing what its inverse is. More clearly from the range of trigonometric functions we can get the domain of inverse trigonometric functions. Since the slope is 3 3 1 you move up 3 units and over 1. To graph the sine function we mark the angle along the horizontal x axis and for each angle we put the sine of that angle on the vertical y axis.

It has been explained clearly below. Inverse functions swap x and y values so the range of inverse sine is π 2 to π 2 and the domain is 1 to 1. See how the angles are on the y axis this time instead of on the x axis like they were for the sine function. Each of the trigonometric functions sine cosine tangent secant cosecant and cotangent has an inverse with a restricted domain.

These points are the extreme values of the inputs. Learn about other interesting functions such the inverse or hyperbolic trig functions. The same is true for sine and inverse sine and for tangent and inverse tangent can you see this in the graphs above. In this post we study the graphs of inverse trigonometric functions.

The figure shows what the graphs of inverse sine and cosine look like. They are mirror images about the diagonal. The y values of the graph represent the angle measures. This means that when we re actually working problems using the inverse sine function we ll be limited to quadrant i and quadrant iv location is everything as they say.

Already we know the range of sin x. The slope intercept form gives you the y intercept at 0 2. The inverse is used to obtain the measure of an angle using the ratios from basic right triangle trigonometry. The graphs of y sin 1 x and y cos 1 x.

As we can see from the graph of the sine function many different angles. The inverse of sine is denoted as arcsine or on a calculator it will appear as asin or sin 1. The result as seen above is a smooth curve that varies from 1 to 1. The points indicated on the graphs are at x 1 and x 1.

Curves that follow this shape are called sinusoidal after the name of the sine function. Domain of inverse trigonometric functions.