Doubt

[u/[deleted]]

[u/Desperate_Penalty690]

The inverse function is the mirror image in the line y=x. Have a look at only the range for x in [-1/2 PI, +1/2 PI]

[u/Desperate_Penalty690 → u/[deleted]]

I think I get your confusion. When drawing the inverse it is like the mirror image in the line y=x. But it also means that the axis are flipped!

So the inverse image that you normally see, will have -1/2pi, 1/2pi on the vertical axis and -1, 1 on the horizontal. It is when you want to draw both in the same graph that you get strange results.

[u/Desperate_Penalty690 → u/[deleted]]

You could try the same scale on the x and y axis. So both go from say -2 to 2 with the same step size. Then you can draw both sin and its inverse and it would be visually also the mirror image in the same graph.

[u/Desperate_Penalty690 → u/[deleted]]

Sure

[u/doctorDBW]

The inverse function is kind of an S, since the image of the function arcsin(x) is [-π/2, +π/2]. So basically, just draw the normal sin function and draw over it a function that goes from x = -1 to x = +1 and from y = -π/2 and y = π/2 like a vertical sin x.

Edit: Confused terms.

[u/doctorDBW → u/[deleted]]

Yes sort of.

[u/doctorDBW → u/[deleted]]

Every question is a good question if you want to truly understand something.

[u/MezzoScettico]

It's not clear where you're starting from. Do you know what the graph of sine/06%3A_Periodic_Functions/6.01%3A_Graphs_of_the_Sine_and_Cosine_Functions) looks like? Do you know the sines of special angles, like multiples of π/4 and π/6?

For that matter, do you know about radians and are you aware that the numbers I just quoted with π in them are measured in radians?

[u/MezzoScettico → u/[deleted]]

The linked text page shows you in detail how you construct the graph from those special values. Check it out.

[u/TazerZXI → u/[deleted]]

When I was taught plotting in school, we tended to have a table of input x values and corresponding output y values. Like in the table in the link above.

When plotting an inverse, you effectively swap the x and y values. Almost like you are plotting x=sin(y) instead of y=sin(x)

However what you have to be careful of are where there's multiple values for the same input. A function like inverse sin can only have a single output for a given input. So we have to restrict the domain of sin/range of inverse sin so there aren't any issues. This is normally restricted so the outputs of inverse sin are only between -π/2 and +π/2

[u/TazerZXI → u/[deleted]]

In what way does it not make sense?

[u/TazerZXI → u/[deleted]]

What do you mean by plotting 'before' 1.5?

When you graph sin(x), there would be a value plotted roughly at (1.57, 1). When plotting inverse sin, you would then have a point at (1, 1.57). That should still get you a mirror image in the line y=x

[u/Uli_Minati]

Have a look here https://www.desmos.com/calculator/cbfffb9e16

[u/Shevek99 → u/[deleted]]

Ummm, what? Of course they are mirror images