Problem. Show that the following are all equal to each other:
...See MoreI don't believe I've ever started a thread here, but since I was here a few moments ago replying to someone else, I thought I'd toss out a neat trig. result that could easily be worked into a trig. or precalculus class as an application of the sine angle subtraction formula.
Problem. Show that the following are all equal to each other:
tan(99 degrees), tan(999 degrees), tan(9999 degrees), tan(99999 degrees), etc.
Hint/Proof-Outline. It suffices to show that each of these is equal to tan(99 degrees). Now observe that the equation "tan(999...9 degrees) = tan(99 degrees)" is equivalent to an equation of the form AB - CD = 0, where A,B,C,D are the sine or cosine of 99 degrees or 999...9 degrees. Use the sine angle subtraction formula to compress this and then note that the angle you're taking the sine of is an integer multiple of 180 degrees. Finally, work backwards from this to get a proof of what we wanted to prove.
9999 = 9000 + ...See MoreOn 7/31/12, math passerby wrote: > Problem. Show that the following are all equal to each > other: > > tan(99 degrees), > tan(999 degrees), > tan(9999 degrees), > tan(99999 degrees), etc.
There is an easier way to show this than the way I suggested earlier.
999 = 900 + 99 = 5(180) + 99,
9999 = 9000 + 999 = 50(180) + 999,
99999 = 90000 + 9999 = 500(180) + 9999, etc.
From this it follows that: 999 degrees is an integer multiple of 180 degrees added to 99 degrees, and hence tan(999) = tan (99); 9999 degrees is an integer multiple of 180 degrees added to 999 degrees, and hence tan(9999) = tan (999); 99999 degrees is an integer multiple of 180 degrees added to 9999 degrees, and hence tan(99999) = tan (9999); etc.
2) What are your going to ...See MoreI had the same problem in middle school, but instead of a grey plastic tote the stuff (going back about 30 years) filled all six cabinets in the room.
1) I don't know K, but I'd say keep more than you think you will need. Will you always have 12 kids? How about 24-30 in 1st or 2nd grade if you get moved?
2) What are your going to do with them? It seems wasteful to dump them. I made a list and emailed it to everyone in the district and said first come first served -- most things disappeared within two days.
3) If they are all in one big bin, what's the difference between you keeping one full bin or one half full bin?
4) If you are new to this, you may not know what you will need or end up finding a great use for. I would try to keep it all for at least a year or two, until you have figured it out.
Does anyone know if NY State has published any books/materials for the new Common Core Standards? I had heard that publishers were throwing nonsense out there for months but NY State was advising not to buy them because the "real" materials would not be out until July/August.
I know some of you have been patiently waiting 'till the countdown is over. I am happy to announce that after many sleepless nights, our website is now running.
I developed [link removed]).
I really hope that through this website, I could extend my collection of math resources, especially AP Statistics, to teachers who are looking for math presentations that they could use in their math instruction.
Let's start to "number bend" and make use of technology for a more exciting and creative math instruction.
I know what you mean about teachers who simply want a job. Observing how my son has been taught math (rather poorly) has re-ignited my passion for it. I have had to undo some his teachers' damage over the years, as many seem to only teach the 'how' and not the 'why'. They were teaching him to plug numbers into a formula without teaching why the formula exists in the first place.
Growing up on the Space Coast of Florida with plenty of engineers and NASA workers, I was lucky to have fantastic teachers throughout my childhood...people with a real passion and excitement for math and science who truly cared and knew how to prepare us for the next 5 years of study (as one of you emphasized).
When it comes to continuing my major in mathematics, I'm worried that picking up where I left off might be extremely difficult, if not impossible, since I took Calc 2 back in 1991. Any advice on that? Most colleges will not allow you to re-take the same courses.
On 8/16/12, Todd wrote: > Hi all - I'm hoping some of the current math & computer > science teachers can give me some good advice. I originally > started my degree in 1990 at Lenoir-Rhyne University in NC. > I started out with a Math & Physics dual major and > completeed Calc 2 and Physics 2 honors before I became lazy > and switched majors. To make a long story short, I switched > majors numerous times, ended up joining the Army, and here > I am 19 years later...still 18 credits shy of my degree. I > have plenty of time to finish before retiring from the > military. My question is this: With a goal of teaching > middle or high school math, physics, and/or computer > science when I get out of the Army, would it be viable to > go ahead and consolidate my various courses into a BS in > Liberal Studies? If not, would a degree in computer science > be preferable?
Yes, there are a LOT of online resources available. Have you checked out MIT's opencourseware? They have videotaped courses on Linear (Matrix) Algebra, Diffy-Qs and the Calculus. There is even a free book on the Calculus available for download (it's written by Gilbert Strang, the Lin Alg prof).
Other schools have video courses as well (UC Stanford, for ex.)
On 8/20/12, Todd wrote: > > Thank you all very much for the input - I certainly appreciate > it! > > I know what you mean about teachers who simply want a job. > Observing how my son has been taught math (rather poorly) has > re-ignited my passion for it. I have had to undo some his > teachers' damage over the years, as many seem to only teach > the 'how' and not the 'why'. They were teaching him to plug > numbers into a formula without teaching why the formula exists > in the first place. > > Growing up on the Space Coast of Florida with plenty of > engineers and NASA workers, I was lucky to have fantastic > teachers throughout my childhood...people with a real passion > and excitement for math and science who truly cared and knew > how to prepare us for the next 5 years of study (as one of you > emphasized). > > When it comes to continuing my major in mathematics, I'm > worried that picking up where I left off might be extremely > difficult, if not impossible, since I took Calc 2 back in > 1991. Any advice on that? Most colleges will not allow you > to re-take the same courses. > > > On 8/16/12, Todd wrote: >> Hi all - I'm hoping some of the current math & computer >> science teachers can give me some good advice. I originally >> started my degree in 1990 at Lenoir-Rhyne University in NC. >> I started out with a Math & Physics dual major and >> completeed Calc 2 and Physics 2 honors before I became lazy >> and switched majors. To make a long story short, I switched >> majors numerous times, ended up joining the Army, and here >> I am 19 years later...still 18 credits shy of my degree. I >> have plenty of time to finish before retiring from the >> military. My question is this: With a goal of teaching >> middle or high school math, physics, and/or computer >> science when I get out of the Army, would it be viable to >> go ahead and consolidate my various courses into a BS in >> Liberal Studies? If not, would a degree in computer science >> be preferable?
Hi I was just wondering if I need a Graphing Calculator for class.... I'm going to take Algebra 1 Accelerated in 7th grade... About Algebra 1 chapter 7...
The only person who can really answer that question is your own teacher. However, it sounds like you are a strong math student (good for you!). Even if a graphing calculator is not required, it would still be a wonderful tool for you to have. There are good sales at this time of year. My recommendation is tto buy one if you can afford it. If there's any way to check with your teacher first, that would be wise because then you'll know which model would be best for your class.
I hope you have a great year.
On 8/19/12, Daniel wrote: > Hi I was just wondering if I need a Graphing Calculator for > class.... I'm going to take Algebra 1 Accelerated in 7th > grade... About Algebra 1 chapter 7... > > Thank You!
On 8/19/12, Daniel wrote: > Hi I was just wondering if I need a Graphing Calculator for > class.... I'm going to take Algebra 1 Accelerated in 7th > grade... About Algebra 1 chapter 7... > > Thank You!
There is an easier way to show this than the way I suggested earlier.
999 = 900 + 99 = 5(180) + 99,
9999 = 9000 + ...See More