## How should I memorize radians in the unit circle?

One of the things that I always screw up is the unit circle. I’ve never paid attention in precalculus, so this is my Achilles Heel. I can optimize and do related rates, but I just can’t memorize the unit circle.

I’ve got the coordinates memorized, because once I find the coordinates in the first quadrant, the other three quadrants are easy to find. I just can’t memorize the radians.
If I had to solve a simple equation such as cos (7π/6) without a calculator, I wouldn’t know that it would be -(√3)/2 because I wouldn’t know where 7π/6 is on which quadrant.

Yes, there are only three families of angles, plus the four quadrantal angles.
➥ The quadrantal angles are the easiest, so you’re probably not even having trouble with them, but just in case: Start, of course, at 0, and you can count by π/2’s: one π/2, two π/2 (=π), three π/2, four π/2 (=2π).
➥ The π/4 family is easy too. You have one, three, five and seven π/4 in Quadrants 1 through 4. Notice odd multiples of π/4. And you know they share the (±√2/2, ±√2/2) coordinates depending on their quadrant.
➥ The π/6 family is the short family, and the π/3 family is the tall family. Closest to the x-axis is short, farthest from the x-axis is tall. The short family (π/6) is only ½ unit tall, while the tall family (π/3) is √3/2 units tall. You know that √3/2 is always paired with ½ in the coordinates
➥ Finally to the names of the angles: Count the π/3 angles, and the only one you skip is 3π/3 because it’s really just π. π/3, 2π/3, 4π/3, 5π/3 in quadrants 1 through 4.
➥ The π/6 family is the hardest to memorize, but the names of the π/6 angles are pretty much any number that DOESN’T reduce with 6!! 1, 5, 7, 11, so we have π/6, 5π/6, 7π/6, 11π/6 in quadrants 1 through 4.

And here’s one other dumb trick. In QII, the numerator is exactly one less than the denominator, and in QIII, the numerator is exactly one more than the denominator. In QII, you have 2π/3, 3π/4, 5π/6. See!? And in QIII, you have 7π/6, 5π/4, 4π/3.

## What is the best advice for conceiving?

My husband and I have been trying to conceive for 6 months.. this will be our first child. I have been using an ovulation calculator and also ovulation kits. We have been having sex on average every other day to once every three days ensuring to have sex around ovulation. We still have not conceived. What advice does anyone have please?

## Can someone graph a basic but cool picture on a graphing calculator using polar coordinates?

For my math class, I need to graph a design/picture using polar coordinates. I was thinking like a smiley face, butterfly, bumble bee, etc etc. Does anyone know of the equations for a picture?

Before we begin theta means that symbol that looks like an 8 that you get when you press the X key in polar mode.

You can try to graph some sets of graphs
Like this one: (FYI „A“ and „B“ are constants)
Y1= a+sin(2*pi*theta)
y2= a+sin((2*pi*theta)+2*Pi)
and then do the same but use +4*pi [instead of +2pi], then +6pi, then +8pi and then +10pi
It should look like this:
http://www.maplesoft.com/applications/view.aspx?SID=1630&view=html&L=G
[the uh orange basket weaving one]

But if you don’t want to do that many graphs here’s a basic formula for making polar flowers in general:

a*sin(b*theta) OR a*cos(b*theta)

A will be how large your flower will be… The larger A is the larger your flower will be
B is the number of petals HOWEVER if B is ODD the number of petals = B if B is even the number of petals = 2B

So 7sin(4theta) will give you a graph that is about 14 units in diameter, and has EIGHT petals

Sin and cos look very similar, but try layering them for effect.

Or if you’re just looking for something incredibly simple:
Y1=theta

that’s it! That will give you a spiral

Have fun and good luck

## What is the sign of a product of an even number of negative factors; what does this mean?

What is the sign of a product of an even number of negative factors?

I had a question that said that what does this mean … even number?

I had another one that said the same thing but it said „odd number“ instead of even number…

– * – = + … Eg (-1)*(-1)= +1 (google calculator will tell you this.)

– * – * – = – … And (-1)*(-1)*(-1) = -1

-*-*-*- = + … And (-1)*(-1)*(-1)*(-1) = +1

-*-*-*-*- = – … And (-1)*(-1)*(-1)*(-1)*(-1) = -1

so, if there’s an even number of negative terms, the result is positive.
If there’s an odd number of negative terms, the result is negative.

Btw, you can scatter positive terms along the way.
That won’t change the sign.
It’s only the negative terms that you have to count. SO,

-*+*-*+*- = – … And (-1)*(+1)*(-1)*(+1)*(-1) = -1

## How long would it take to travel to the next star system at 10x speed of light?

Ok sounds a little odd but scientist are now saying it may be possible to create a ship that can warp space in order to achieve FTL, not only that but they say it may be possible to go 10 times the speed of light. So how long would it take to get to alpha centari roughly 4.1 light years away. I know the math is simple but my calculator does not deal with numbers that large so I turned to the I Internet.

T = t/√(1 – 10²)

T = t/√-99

T = t/9.95i

T = 4.1/9.95i

T = 0.412/i years ship time.

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