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The law of sines can be tricky when you are only given the information of two sides and one angle because there is a possibility of two answers. How can this be you might ask, well if the opposite side from the given angle is greater than the vertical height of the triangle then it is possible that the unknown side could make either an obtuse or an acute. Cannot just use the law of sines to solve the triangle because it won't consider the possibility of a second triangle. This may be easier to understand through a picture. In this picture you can see that the if the length of the opposite side length is longer than the height of the triangle then two triangles can be made. If the opposite length is shorter than the height than a triangle cannot be made.
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After attempting this project I was able to see how the unit circle relates to the x/y plane. At the beginning I was confused by how the unit circle related to anything, for I understood the unit circle in how it relates to radians but not how it relates to a graph. After working with Ian for a few days we were able to see how the different trig functions would produce different results. We were able to recognize how Tangent, Cotangent were similar, we also knew to look out for vertical asymtotes for those trig functions. We could also see how the two special triangles (40-60-90, and 45-45-90) triangles related to sine, cosine, secant, and co-secant. Using the special triangles was a big help in being able graph the points given to us. After doing a couple to practice before the test Ian and I were able to visualize the look of the graphs that we were plotting points for. Many people don't use or understand radians, because to non-mathematical thinkers radians are written in almost a foreign language. So most people when they don't know what things are wikipedia it. To save time the wikipedia definition is "a unit of angle, equal to an angle at the center of a circle whose arc is equal in length to the radius". What does this really mean? one radian is equal to the length of the radius of a circle. This then relates to the radian circle (not only because the word radian is in it) a radian relates because the radians similar to degrees make up a circle (2pi is 360, pi is 180). Now why does this have any meaning? Since it contains pi doesn't that make it a pain to use? Well no as previously stated 2pi is 360 degrees, well this looks familiar to the circumference formula 2piR now why is this so? Radian circle is a circle placed on the x-y plane with a radius of one and on a circle with a radius of one to make it completely around the circle is 2pi, to find the circumference of a circle that has a smaller or larger circumference you would need to multiply the radius by the circumference of the radian circle. No what is the point aren't degrees more common wouldn't it be easier to just stay with degrees? Well no although it is easier to picture the angle measure radians are more mathematically pure because rather than having to round the decimal, an exact measurement can be discovered by using radians. Please research formulas for computing loan interest. Please look for formulas that compound the interest in different ways. Please research different types of college loans: government subsidized, non-subsidized, credit union loans, and bank loans. For simple interest a formula that can be used is: P (1 +rt) P= Principal or amount of loan R= Rate of interest or percent T= Time at which the loan is applied This formula will calculate the amount of interest you will owe on a loan after how ever long you have the loan. To calculate the the percent of interest rate you would use: (i / P) x number of days To calculate compound interest the formula that can be used is: A=P(1+r/n)^(nt) A = the future value of the investment/loan, including interest P = the principal investment amount (the initial deposit or loan amount) r = the annual interest rate (decimal) n = the number of times that interest is compounded per year t = the number of years the money is invested or borrowed for Government subsidized loans: Are available to Graduate and Undergraduate students, and is based off of a student's financial need. The student's college will determine the amount of the money that can be borrowed and the amount will not exceed the financial need. The U.S. Department of Education pays the interest on a Direct subsidized loan. A direct non-subsidized loan is different in that the student is required to pay the interest rather than the U.S. Department of Education. Credit Union Loan: are loans that are not included with Federal financial aid but have a competitive interest rate as well as flexible repayment terms. Usually take within 20-25 years to pay back. Bank Loan: most common type of loan, provides medium to long term finance. The bank sets a fixed period for which the loan is provided. The interest is the timing and amount or repayments.
When finding the zeros of a function the trick is to factor the function. To factor you divide out numbers or variables that you know are the least common multiple (LCM) you can do this by graphing the function and finding the "easy zeros" or by seeing a common variable such as 3x-9 a three can be factored out because both variables contain a three, there for the completely factored function would be: 3(x-3). Although it looks like I just pulled out the three from both sides what really happened was I divided 3 out of the equation 0=3x+9 to make 0/3=x+3 and then you move the three back over to make 0=3(x+3) Although in the previous example it was obvious that both variables had a three in common some are less common and that is why it is helpful to graph more complex functions. After graphing the functions you can find the easy zeros, these are zeros that are nice whole numbers. If I were to graph a function and I got a zero of -3 then I would know one of the factors of the function is (x+3), the signs to answer the question "what would make -3 turn equal 0?". When looking at a polynomial that is put to a power, that power is able to tell us how many x intercepts we are expected to find. But be careful some intercepts are imaginary numbers, or appear twice. If a an x-intercept is also a maximum or a minimum it tells us that the x-intercept is a repeated factor. For a maximum or minimum the polynomial was raised to an even power. Although the power does not always show us how many factors the polynomial will have because I believe that the basketball will hit the backboard and go into the basketball hoop because the given model below shows the predicted placement of the basketball.
The provided graph shows a exponential function. Both the domain and range of this function are all real numbers greater than zero.
After reading given articles relating to the sale of I-tunes songs in the given years I predict that the growth of sale in I-Tunes songs will continue to increase exponentially, at the apple store continues to create new products. After reading the article my prediction on the domain and range does not change. There is a problem with extending the points because if you plot points based on a trend because the numbers are so high that the scale will be hard to determine most points. There is a possibility that the points could be wrong given no human can predict the future there could be a drop in sales for any reason.
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AuthorLindsay is in Math Class Archives
February 2017
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