Power of the Polar Equations

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What are polar equations actually used for? They are actually used for navigation, using the angle and distance from the object (center). But, they often use angle measures instead of radians in giving directions.  In addition, radial symmetry uses the polar coordinate system as the central point acting as a pole.  Hence, everything is revolved around the pole.  In addition, radially asymmetric systems are modeled with polar coordinates.  For instance, a microphone uses a pattern that illustrates the response of the sound from a certain direction.  These are usually explained through polar curves.

In addition, they are used to make fun art!!

Lesson 10.8

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Today we learned about the polar equations of conics, which includes ellipses, hyperbolas, and parabolas.  There are some very important equations you need to do in order to find the polar equations.

• r = ep/ 1+esinθ
• horizontal directrix that is above the pole (positive y)
• r = ep/1-esinθ
• horizontal directrix that is below the pole (negative y)
• r = ep/1+ecosθ
• vertical directrix that is on the right of the pole (positive x)
• r = ep/1-ecosθ
• vertical directrix that is on the left of the pole (negative x)

These are the equations you will use in order to find the conic equation with the given information you are given.

In addition, you must be able to identify an ellipse, parabola, and hyperbola for each conic equation. You can determine this through the eccentricity (e).

ellipse: e< 1

parabola: e= 1

hyperbola: e>1

Lesson 10.6

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Today we learned about Polar Coordinates.  Basically, this is another form of graphing other than using the x and y axis.  In particular, this graph uses circles and radians to graph plot points.  Here is some vocabulary commonly used in polar coordinates.

r = directed distance from O to P
Theta = directed angle, counterclockwise from polar axis to segment OP.

In addition, there are coordinate conversions you need to know in order to be able to understand your points.

Polar to Rectangular Conversion
During a Polar to Rectangular Conversion, you will be given points (r, theta) and you will plug them into the corresponding coordinate conversion equation. (x = cos, y = sin)

Why Calculus?

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I've always wondered why certain math subjects are needed for specific occupations.  For instance, Calculus is needed to become a Pediatrician...um what?  I know this because I am very interested in becoming a pediatrician and when I looked at what college courses were necessary, Calculus was one of them!  So I decided to search on what's so cool about Calculus.
Well, to start of you actually don't REALLY need Calculus to be a Pediatrician.  You actually need it to go to Med School.  Calculus is a concept that is found in many sciences, such as Physics and Chemistry, which are subjects that are part of the MCAT (Medical College Admission Test).  Though one can go through the MCAT using Algebra-based concepts, one will not receive an adequate score compared to one who uses Calculus-based concepts.  Getting a good score on the MCAT is important because it is a ticket to get you into a Medical School, and getting into Medical School is how you become a Pediatrician.
All in all Pediatricians don't need Calculus, but you DO need Calculus to become a Pediatrician.

Lesson 10.3

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Today we learned about hyperbolas.  Hyperbolas are a set of all points (x,y) the difference of whose distances from two distinct points (foci) is constant. Hyperbolas consist of two parabolas that are equal, but are positive and negative. The vertices are equidistant from the center.

Here are some equations you need to know.

Your asymptotes are used so that you know the boundaries of your hyperbolas. 

Here's an example:

Here's how to do it!

Step one: Turn the equation into standard form.

Step two: Find your a, b, and center (h,k)

Step three: Find your vertices using a and b.

Step four: Draw a square around your vertices, this will help with your asymptotes.

Step five: Place your asymptotes by drawling lines from the corner of your square through the center.

Step six: Find your foci.

PI DAY!

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Today (well, tomorrow) is Pi Day, March 14, 2014.  Pi, is a Greek letter that represents a constant. It is most frequently used in equations such as the circumference or area of a circle.  Pi has been known for over 4,000 years and nobody really knows who discovered it.  It has so many digits after the decimal that it's impossible to memorize every digit of pi.  Since Pi Day is such a glorious holiday in the Math World, and our small town of MathLand, I found a Scavenger Hunt that is based off of Pi!

Here are the answers I got.

3. cylinder and sphere

1. Savannah, Georgia

4. E,S,I,O

1. Indiana 1897

5. C = 2 pi r (circumference of a circle) A = pi r^2 (area of a circle)

9. target, pepsi, at&t, no smoking

2. Round Rock, Texas and Cannon Ball, North Dakota

6. Colorado, Florida, Idaho, Kansas, Kentucky, Minnesota, Missouri, Montana, and Nebraska

5. Golf, Volleyball, Basketball, Softball, Baseball

3. Albert Einstein 1879

5. Around the World in 80 Days

8. M&M's, Skittles

9. Ring of Fire, Joy to the World, Here Comes the Sun, Circle of Life

7. allrecipes.com/recipes/desserts/pies

Lesson 10.2

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Today we learned about elipses. Elipses are a set of all points (x,y) the sum of whose distances from two points fixed points is constant. The equation of an elipses is determined through its major axis.  The major axis is where the elipses is longer in length.
Here are the equations and terms you need to know for elipses!

Here's an example!

Lesson 10.1

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Today we learned about parabolas.  A parabola is a set of points (x,y) that are equidistant from a fixed line (directrix) and a fixed point not on the line (focus). There are two equations you need to do and they correspond with which way the parabola is facing and opens up.
When a parabola is vertical it is equal to (x-h)^2 = 4p(y-k).
When a parabola is horizontal it is equal to (y-k)^2 = 4p(h-k).
P = the distance between the vertex and the focus = the distance between the vertex and the directrix
Find P with the coefficient of the equation equal to 4p.

Here's an example!

Human Calculator (Not Miss V)

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Even though we all think that Miss V is the Human Calculator, SHE'S NOT! It's actually a man named Scott Flansburg.  He goes around the world to show that calculators aren't everything, that it's really all about his brain.  He does everything that you can use on a calculator, even square roots and fractions!  He even beat a room of mathematicians at SDSU. It's actually so crazy how he is able to recite a list of numbers, it's amazing.  I don't know what he does everyday, or how he is able to calculate such things faster than a calculator, but obviously I'm a little behind on my math compared to him.  It's even said that maybe a total of 6 people IN THE WORLD, which consists of billions of people, have the talent Flansburg does.  You should watch this video and see this unique talent for yourself!

Exploring Data

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Do you remember mean, median, and mode? Well, you should because it's one of the simplest things in math and is actually used very often.  Even in many jobs today.  But let's just review. Mean is the average of a set of numbers, the median is the middle number when they are put in order from least to greatest, and the mode is the number that occurs the most. Finding mean, median, and mode is what central tendency is! Easy peasy. Another thing used with mean, median, and mode is measures of dispersion.  This is when you find variance and standard deviation. First you find the mean, then you plug in the numbers into the variance equation, and then find the square root. And that's how you find standard deviation!

Probability

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This week we learned about probability. Probability is the likelihood of something happening through the situation and information at hand. Probability deals with outcomes, sample space and an event.  The outcome is the result of the experiment, the sample space is the possible outcomes, and the even is the subcollection of the possible outcomes. The probability of an event is described as the event over the sample space. An independent event occurs when order does not matter and a occurrence has no effect on the second occurrence. For instance when a marble is taken, but then put back, the event is not changed.  Probability questions are usually word problems, and they just take a deeper understanding of the problem.  Then, you can use your common sense, or the equations to find your answer.

Probability of a Complement: P(A) = 1 - P(A)

Probability of Independent Events: P(A and B) = P(A) x P(B)

Probability of an Event: P)EP = n(E)/n(S)