SP #7: Unit Q COncept 2

In this SP I will show how to write and solve  a problem using two methods: The Identities, ( Ratio, Rational, Pythagorean) and the famous SOHCAHTOA.

SOHCAHTOA

In the image above you can see the work for finding the 6 trig functions using the method of SOH CAH TOA. To find the 6 trig functions we use a certain method of SOH which the OH in SOH is represented opposite over hypotenuse, and we substitute it in for the values/ numbers. TO find the CAH or TOH we use the same logical reasoning. As a result we were able to find the reciprocal to find the other 3 trig functions, which where CSC, SEC. COT.

IDENTITIES

In the identity method to find the 6 trig functions, we had to use the ratio, rational, and Pythagorean identities to solve. First we started of with tangent, which was SINE over COSINE, and basic substiitution of numbers,from there we were able to plug in COT, which equaled to 1/ tangent. The we substituted and we got our answer. Then we used the Pythagorean identity of 1 + tan ^2 theta = Sec ^2 of theta, then we substituted in for tan ^2 theta and then from there we combined like terms to get our answer. To find CSC, we used another Pythagorean identity. Which was 1 + COT ^2 theta = CSC ^2 theta and simplified the same way as finding for SEC.Finally we used the reciprocal identity of CSC and SEC to find SINE and COSINE, from there we basically simplified.

SP#6: Unit K Concept 10: Repeating decimal as a rational number

First, write the decimals in a pattern, like the one that I did below the original problem. Ignore the 2 until the end. We get our "a" sub "1" by the first decimal which is 96/100, and our ratio is 1/100. Using summation notation and the geometric infinite formula we can start plugging in. The summation notation will also use the geometric sequence formula and you already have the ratio and the"a" sub "1". Next will be the infinite geometric series and just plug in (96/100) / 1-(1/100). You subtract the 1 to 1/100 and get 99/100. With (96/100) / (99/100), use the reciprocal of 99/100 and multiply it to the numerator and denominator. Now you should have 96/99, and this is were you include the 2 from the beginning. Add 2 to 96/99 and your answer will be 294/99 but reduced will be 98/33.

Well in my opinion for this problem your need to pay attention to the reciprocal part. It can be confusing and it's easy to make a mistake here. Also the part when you add 2 to 96/99 because you have to reduce and it can get tricky if you do it wrong.

SP#2: Unit E Concept 7: Zeroes and Multiplicity

This problem is about using zeroes to create a polynomial. The zeroes should also be used to find the x-intercepts and the y-intercept. Finally, it should be possible to find the end behavior and graph the equation. To solve this problem, you should make sure you know how the multiplicity of a zero affects the graph of the equation. A multiplicity of one, for example, means that the graph will go through that point. Knowing the extrema will make the graph more accurate.

SP#3: Unit I Concept 1: Solving an Exponential Equation

 

Let me be honest, solving these type of problems wasn't easy. First you need to understand how to find the values of the following variables. ( a, b, h, and k). This is because they are important  to finding the asymptote, domain, and range. You also need to focus on the colored parts of the image, because they are important. They are meant to help you

 

 



Step 1: The equation can determine if the graph lies below or above the asymptote. Since the value of a is negative, the graph lies below the asymptote; then check if the asymptote is vertical or horizontal by checking to see if its a log or exponential. In either case, the equation is an exponential one, and it's asymptote is equal to the k value. Therefore, the asymptote is "y = -4"
Step 2: Now since the asymptote we can say there is no x intercept.
Step3: Solve for the y-intercept.
Step 4: Next; determine the domain and range of the graph. Since this is an exponential equation, the domain is unrestricted. The range, however, depends on the asymptote. In this case, the range is -∞, -4.
Step 5: Label the graph, plug the equation into your graphing calculator and press the buttons labeled '2ND' and 'TABLE'. This will give you a table of all the points on the graph. Select a few, put them in your table, and plot them. Draw the asymptote, connect the dots, now you have solved this exponential equation.

SP#5: Unit J Concept 6: Partial Fraction Decomposition (Repeated Factors ver.)

What is this problem about?
This problem is an example of Unit J, Concept #6. In this concept we learned how to solve Partial Fraction Decomposition (Repeated Factors ver.)

What does the viewer need to pay attention too?
Remember to Distribute carefully when you are multiplying and when you are trying to get the common denominator. Also when you are separating it into parts count the powers.
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SP#4: Unit J Concept 5: Partial Fraction Decomposition (Distinct Factors ver.)

What is this problem about?This problem is on an example on Unit J Concept 5, That is on how to solve partial fraction decomposition with distinct factors.

What does the viewer need to pay attention to?
To remember to distribute carefully and when multiplying when trying to get the common denominator.

SP#1: Unit E Concept 1 - Graphing a quadratic and identifying all key parts