## moongazer 3 years ago Could someone explain to me how to graph of all inverse trigo functions and its properties? or can you give me a website that can help :) Thanks! :)

1. kuraby

wolfram alpha can graph functions for you

2. moongazer

I already know how to graph the graph trigo functions, but not the inverse. :)

3. ash2326

Hi @moongazer this might help http://www.intmath.com/analytic-trigonometry/7-inverse-trigo-functions.php

4. kuraby

Nice website ash. it is like replacing the x values with the y values.

5. moongazer

@ash2326 I already saw that awhile ago. But I can't understand why it works. when you make y=x it gives you the inverse graph.

6. moongazer

How do you also find the other properties? like the period, amplitude, phase shift etc.

7. kuraby

That is true. given a graph x = siny you get the sine curve going up the y-axis.|dw:1347168918572:dw| ignore faults in sketch. But by the vertical line test this graph would not be a proper function. so we have to put boundaries. That graph can only by a proper function when x = -1 up to x = 1.

8. kuraby

So looking at inverse sine, or arcsine: y = arcsinex |dw:1347169164647:dw| the domain of x is -1 to 1, and the range of y is -pi/2 to pi/2

9. moongazer

does it have a period also? or amplitude?

10. kuraby

The function does not repeat, so no period. no amplitude in the traditional sense. amplitude refers to the regular sine functions that do repeat. If you are referring to the distance in x from the function to the y-axis, same amplitude as y=sinx.

11. kuraby

Not the best of descriptions, but inverse functions tend to be used to find angles. Any reasons on why you would need inverse properties?

12. moongazer

it is our homework :) it says summarize the graphs ans properties of trigonometric functions. why is when you want to graph the inverse, you make it y=x?

13. kuraby

concept of using y = x is to draw a mirror or reciprocal of a given graph. One reason for doing so with trig functions is to find some degree given a length. Usually the question goes what is y= sinx where x is a given degree and y is the desired length. Now the question would be "for what length y does degree x give for function sine? so instead of just saying switch y with x, ask the question: if y = sin(x) then y = sin (?) when y is given. The graphing is to portray all possible values of (?) when y is given. then y becomes our independent variable while (?) becomes our dependent variable. drawing the results becomes a mirrored graph of sin(x) when reflected off the line y = x. as so:|dw:1347173789922:dw|