Joseph asks…

## 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.

Any tips to memorize radians?

### admin answers:

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.

Linda asks…

## 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?

### admin answers:

After sex lay on your back for at least 15 minutes to prevent sperm from leaking out and It helps boost the chances of sperm reaching to the eggs.. Don’t stress over it. Just enjoy it. The gland in the brain that regulates the hormones of ovulation doesn’t function as well when you’re stressed, which means you may ovulate later than usual or not at all that cycle. Even spice of your sex life a little and try new positions. I see that you are using an ovulation calculator and kits so along with that watch for changes in cervical mucus. Just before ovulation, you might notice an increase in clear, slippery vaginal secretions and after ovulation, when the odds of becoming pregnant are slim, the discharge will become cloudy and sticky or disappear entirely. Ovulation can cause a slight increase in your temperature when you’re fully at rest. To monitor it you need to use a thermometer specifically designed to measure basal body temperature. Take your temperature every morning before you get out of bed and plot the readings on graph paper or in a spreadsheet. Eventually, a pattern might emerge. You’ll be most fertile during the two to three days before your temperature rises. The increase will be subtle, typically less than one degree. Make sure you do not go any longer than 2 days without sex but also don’t have sex to much because his sperm count will drop and the best time to have sex would be in the morning time. Maintain a healthy weight, include moderate physical activity in your daily routine, eat a healthy diet, limit caffeine and manage stress. The same good habits will serve you and your baby well during pregnancy and Your health care provider can assess your overall health and help you identify lifestyle changes that might improve your chances of a healthy pregnancy. Preconception planning is especially helpful if you or your partner have any health issues. Vitamins are good when trying to get pregnant,such as folic acid and prenatal vitamins. You could find them at walmart for usually less than \$5. When trying to conceive you need to avoid smoking, drinking, vaginal lubricants, very strenious excersice and some medications. Tobacco affects cervical mucus, which can prevent sperm from reaching the egg. Smoking may also increase the risk of miscarriage and deprive your developing baby of oxygen and nutrients. . If you need a lubricant, consider mineral oil or canola oil or ask your doctor for other suggestions.Various over-the-counter vaginal lubricants, including K-Y Jelly, can decrease fertility. Saliva can have the same effect.If you’re in your early 30s or younger and you and your partner are in good health, try it on your own for one year before consulting a doctor. Consider seeking help sooner if you’re age 35 or older, or you or your partner has known or suspected fertility issues. Infertility affects both men and women — and treatment is available. Depending on the source of the problem, your gynecologist, your partner’s urologist or your family doctor might be able to help. In some cases, a fertility specialist offers the best hope couples don’t get pregnant right away. Out of 100 couples trying to conceive every month, 15 to 20 will succeed. However, 95% of couples trying to conceive will get pregnant within two years! You can’t control every factor of your fertility, but there are a few simple changes you can make to increase your odds. Avoid trans fat, often found in processed baked goods and sweetened foods. There is some evidence that a diet high in trans fat (especially relative to monounsaturated fat intake) can increase chances of infertility.Avoid questionably prepared raw fish, unpasteurized cheeses, sprouts, prepackaged foods that don’t look fresh, and lunch meats containing nitrates. These foods and other foods that are undercooked or improperly cleaned can lead to food poisoning or illness, reducing your chances of supporting a healthy pregnancy.at a diet rich in organic plant-based foods that includes grains, nuts, fruits, and vegetables. The antioxidants, vitamins, and minerals provided by these foods are thought to improve cellular health and even promote a healthy uterine lining. The right kinds of protein can help boost fertility; tofu, chicken, eggs, and some seafood are high in omega-3 fatty acids, iron, selenium, and other fertility-enhancing components. Consuming full-fat dairy products, such as whole milk or full-fat frozen yogurt, can potentially improve fertility over a diet of only low-fat or fat-free dairy.e your partner to eat foods that promote sperm health. Men should take a multi-vitamin that contains vitamin E and vitamin C, eat a diet rich in fruits and vegetables, and avoid excessive alcohol, caffeine, and fat and sugar intake. And Please be sure to see a doctor. If you have any questions or would like to know more please feel free to email me at samanderic21@gmail.com

Jenny asks…

## 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?

### admin answers:

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

Mark asks…

## 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…

### admin answers:

– * – = + … 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

Mary asks…

## 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.

### admin answers:

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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