I think that's mostly a style or personal preference issue. Many mathematicians like things to look 'elegant'. 2csc(t) is certainly a lot less clunky-looking than 2sec(t)/tan(t). That said, I probably would've left it at 2/sin(t). Not that I'm a mathematician or anything... but I do think that both 2csc(t) and 2/sin(t) are improvements over the original.

If she's got English phonics down, and she speaks Spanish, then learning Spanish phonics and being able to read most anything in 2 weeks sounds quite possible to me (writing would take a bit more work). Though, come to think of it, written text tends to have some words that are rarely used in spoken language, so she'd have to learn those words too (though at the 3rd grade level there probably aren't that many of those words). Spanish phonics is really easy though (probably the easiest out of any language I've learned). Sorry, no recommendations for materials... something phonics and then beginning readers. If you're familiar with All About Spelling, you could make something like that on your own. Or you might be able to find a Spanish phonics app or something.

(((Ellie))) Happy birthday turtles!

With a calculator (computer) it probably hardly matters at all whether you learn trig or calculus at all... I'm pretty sure that there are programs that will find you the answers to equations you put in. Just like with arithmetic. But, you learn it anyway, because the computer thus far doesn't come up with useful questions and equations that need to be solved, and you need a certain facility with the math in order to come up with that stuff and to be aware when the answer the computer gives you makes no sense. Wrt Khan I meant the exercises, not the videos, since you were asking for more practice. I don't think they've got all of calc 1 and 2 yet though.

There's a rule against that.

Hm, not sure Sandwalker is actually coming back (she liked a couple of my posts on this thread from a few days ago this morning).

Suspenders. :leaving:

Comparison of Amazon vs Plus: https://www.thegreatcoursesplus.com/amazonsignaturecollection Does anyone know if there's a list with courses that are on Amazon but not on Plus? Are there any, and if so, which courses? I do like the closed captions (only on Amazon according to this) though...

Btw, as far as retention is concerned... repeated practice, spread out over longer and longer periods of time (so, at first you're going to have to practice something every day, but then you can practice it every other day, once a week, once a month, once every few months, w/e etc... of course, it varies per person and per topic as to how quickly you can spread out your practice, and yes, it's frustrating). (and that's about all I retained from cognitive science, lol)

Khan Academy has a fair number of calculus problems now. So, when I said go back to basics on the other thread, I meant turn the entire thing into stuff involving sin and cos only, and then simplify. Of course, sometimes you can't... but anyway... I think it tends to help.

Not really. You just want to go back to basics with these things. So, you know (or can look it up, but you'd probably want to memorize it) that the sec is 1/cos, and that the tan is sin/cos, and that csc is 1/sin. So, you just plug in those things where appropriate, and then simplify. You probably want to make a habit of trying to simplify stuff whenever you have some equation with one of those things over another one of those things, or one of those multiplied by another one of those... often you can simplify it. (not a fan of sec and csc etc either, which is one reason I'd try to simplify them away if possible, lol) ETA: also, this probably looks a bit less convoluted on paper than typed in a forum post, since on paper you can just cross out certain things etc.

Welcome to the ITT, Sandwalker! Boeja!

One of my deceased family members went by Jac (not 100% sure if that was short for Jacques or Jacob), pronounced "yuck". And I have family members Els (short for Elisabeth (sp?)) and Joke (that one is pronounced "yo-kuh" though). And I think that about sums it up with "names that sound or look funny to Americans".

I have a Robert in my family, and I don't think anyone has ever tried to call him Bob either. Of course, Bob isn't a Dutch nickname, and I'm sure he'd give me a reeeeeealy weird look if I tried. He goes by Rob. ETA: he doesn't give off a Bob vibe either. I think. I'm not 100% sure what a Bob vibe is, but if it is what I think it is, I don't think so.

I don't know if this is a national or a regional thing, but the Y doesn't have a join fee from the 24th-27th. I'm sure they'll waive the join fee on Jan 1st as well, as they seem to have done that every year that I was a member, but anyway... the join fee tends to be more than a month's membership cost, so not having to pay it is neat.

Note to self: should maybe join the Y tomorrow (from today through the 27th they're waiving the join fee - they'll waive it again Jan 1st, I'm sure, but the kids should practice their swimming. Though there is a public pool too... but they don't have treadmills and parents' night out and all that). ETA: and the public pool isn't free either.

Also, the cartridges that came with the printer were supposed to last 1,000 pages, and they (well, the color ones) lasted 4 years I think (not 100% sure when we got the printer). The regular cartridges are supposed to last 1,400 pages, and the high capacity ones 2,100 pages. There's really no point in subscribing to that.

Me too. I declined, stayed home, violined (yay for the 21st century, where you can just google for a minute and find music to print out... I just did Pachelbel's Canon and Bach's Concerto in D minor (1st movement only)), Russianed, and watched tv while eating dinner. I'm surprised DW and the kids aren't back yet. It doesn't show up when I search the pantry. It's the TN221 (regular) or the TN225 (high capacity), in C, Y, and M. It does show an option for "subscribe and save"... but shows the exact same price, which isn't exactly "saving" in my book: https://www.amazon.com/Brother-Genuine-TN221M-Magenta-Cartridge/dp/B00BR3WXS6/ref=cm_cr_arp_d_product_top?ie=UTF8

I have not yet had a baby That's okay, I started researching the whole homeschooling thing before my oldest was born too. ETA: the person who posted that thread has 4 kids ages 3-12 and baby #5 is overdue, in case anyone is wondering why I thought it's funny.

CRTs use a lot of electricity and put off a lot of heat as a result. Which is not a good thing in Texas summer (or spring, or fall).

And by that I mean that she had 3 monitors on her desk. :svengo: Hooked up to just one computer though, iirc.

Ours has a whole bunch of tables inside. I'm just glad that the 3(+?) CRT monitors stayed in Texas when we moved to NY.

My kids eat paper, it seems. Not literally, but the way they turn into zombies "must.have.paper" when we're out of paper... it's quite something. Who knew paper was so addictive?

DW just did the math. Color printing is apparently only 18% more expensive than printing in B&W, so there isn't much of a reason to not print in color (there is, however, a reason to not print things that cover a huge area of the paper, of course).

You can even eat inside a Sonic. Well, at least here you can... I'm 99.9% sure you couldn't in Texas.