To create these two graphs we used the website desmos and used some polar functions. For the first one we only used one, which is r=3sin2theta. For the second one, over 7 different functions were used. This was a very fascinating class period. It was unknown to me that such strange graphs and artwork could be made using pre-calculus.
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For our arduino project we changed the amount of time until one pattern of beeping turns into another (similar to a siren).
float sinVal; int toneVal; int k=0; void setup () { pinMode(8,OUTPUT); } void loop () { while (k< 2000){ for (int x=0;x<180;x++) { // convert degrees to radians then obtain sin value sinVal = (sin(x*(3.1412/180))); // generate a frequency from the sin value toneVal = 2000+(int(sinVal*1000)); tone(8, toneVal); k++; delay(2); }} for (int x=0;x<180;x++) { // convert degrees to radians then obtain sin value sinVal = (sin(x*(3.1412/180))); // generate a frequency from the sin value toneVal = 2000+(int(sinVal*1000)); tone(8, toneVal); delay(5);} } URL of video https://drive.google.com/a/slsharks.net/file/d/0B6Ep8JcC1gm_dXZYR0dSUDVPVEk/view You can use the unit circle to find the radians of certain degrees. You can find the sin, cos, and the tan of angles as well. It can also be used to find which quadrant any of these are in. The unit circle makes it easy to convert between radians, angles, and cos, sine, and tan.
Government subsidized loans- The federal government pays the interest of student loans while you are in college.
Unsubsidized loans- Government does not pay the interest. Bank loan- A amount of money is loaned with interest from a bank to a borrower. INTEREST RATES - Subsidized and unsubsidized are 4.66%. Bank loans interest can differ. Example of a subsidized loan- (for this example imagine 20,000 is borrowed) 20,000(1+.0466)^10 = 31,538.22 = 262 dollars a month for 10 years. It would take 41 folds to reach the moon. You couldn't fold a piece of paper that many times, or find a piece of paper large enough to get to the moon. It would be infinitely small. Its unrealistic, but yes it matters.
What are limits?- How close something gets to a number.
How can we tell if a limit exists?- If it isn't approaching -1 from the left or 1 from the right. How do limits help us explain function behavior at points of discontinuity?- They help show the behavior of the discontinuity as it reaches the point of discontinuity. Connection between factors and zeroes: If you set the factors equal to zero it helps you find the zeroes to solve the problem.
How division helps us factor polynomials: Finding the easy zeroes is easy enough, but finding the other zeroes is not very hard if you use synthetic division to find the remaining zeroes. How does the degree of polynomial helps us to predict the number of zeroes: Does that tell us the number of factors: We graphed y=x^2 on a graph. Then we graphed the inverse of that. Lastly we drew a dotted like along y=x. When we folded the paper the two inverses matched perfectly.
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April 2015
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