Does my working out check out?

[waxen umbra]

Where did you get equation 1 and what do the parameters represent?
(This is rhetorical, by the way. I do know the answer and you have made a mistake.)
Edit for posterity just in case: I was wrong here.

[waxen umbra]

Where did you get this?

Oh, my bad. I was wrong.

You're good.

I was expecting this formula to show up in factored form.

I really don't like when it's written this way, but it's fine

A good habit, by the way, is to plug in a few sample values

like 0.01 and 0.02

Because you know what they should give, and it's pretty easy to check if it works out.

I would write it as sin(k (x-d))

because then d is the amount that it is actually shifted on the graph

So that would be sin(100pi(x-.005))

yeah, that's my preferred form

But you should use the one that makes sense to you

I mean, I certainly understand and can use both. But it takes me a moment to think through it the other way

You want to shift it by a quarter of one period

one period is .02

so you take one quarter of that

d=0.02/4

Yeah

you're shifting the sine wave before compressing it

I like to compress first and then shift

but there's no right way

You're welcome. Sorry for my early mistake.

type .solved