SP#7: Unit Q Concept 2: Finding All Trig Functions When Given One Trig Function and Quadrant

This SP8 was made in collaboration with Jennifer Guerrero. Please visit the other awesome posts on their blog by going here.

Solving using SOH CAH TOA: 

  

* We used Pythagorean theorem to find the hypotenuse of the triangle.

*making sure to always rationalize a fraction when needed. (ex: cos and sin)

Solving using Identities: 

*we first found what quadrant it lyed on, in order to know which answers were to be positive and which were negative.  (Short cut: All Students Take Calculus)

*we used reciprocal identities to find all but sin. 

* for sin we used a Pythagorean Identity: sin^2x+cos^2x=1

* once again never forgetting to rationalize!!

The viewer needs to pay close attention when solving with identities which ones can be used according to the givens given. Keeping in mind that we can only have one unknone trig function within an identity. Also a key part is never to forget to rationalize! Another thing is that the quadrant it lyes on determines which answers are positive or negative, watch out for the signs. 

SP#6: Unit K Concept 10: writing a repeating decimal as a rational number using geometric series (NO CALCULATOR)

In this picture you will be learning how to convert a repeating decimal into a rational number using the geometric series. The viewer should pay close attention to what happens to the number after the decimal. How it is set aside till the end of the problem. In the end adding it to the answer you have gotten. Also it is very important to make sure the answer gotten is completely reduced. 

SP5: Unit J Concept 6: Partial fraction decomposition with repeated factors

This problem deals with solving partial fraction decomposition with repeated factors. The viewer needs to pay special attention to the repeated factors, they must count up the powers and include the factors as many times as the exponent. They should also be very careful with their signs, whenever distributing or substituting. Another important thing is that the answers gotten for a, b, c, etc, are put in the split up fraction from the beginning. Also the more letter involved the more equations there will be. These are the most important things to keep in mind when doing the problem. :)

SP4: Unit J Concept 5: Partial fraction decomposition with distinct factors

   This problem problem involves partial fraction decomposition of distinct factors. The viewer should pay close attention to the instructions for the calculator, and that when you go 2nd quit and then 2nd matrx you go to math all the way down to RREF then continue the steps. Something else would be to be very careful with your signs and everything plugged into the calculator, because one tiny mistake can cause you to get everything wrong. We don't want all this work to go to waste and start all over so be careful. Another thing would be to always forget to get rid of the x's when you have grouped like terms.

SP# 3, Unit I Concept 1: Graphing exponential functions and identifying x-intercept, y-intercept, asymptote,domain,range (4 points on graph)

 In this problem we will be Graphing exponential functions first by identifying a,b,k,and h with the help of the equation y= (a)(b)^(x-h)+k and identifying x-intercept by setting y equal to zero , y-intercept by setting x equal to zero, asymptote by y=k, domain not having any restrictions because it's a exponential function ,range (4 points on graph)The viewer needs to pay special attention on the equation and how every number represents a certain letter. Another thing is that the asymptote is y=k
and is a horizontal line. As seen in finding the x intercept we do not have one because you can't take the log of a negative number. To find the y intercept you basically just substitute x for zero. Lastly the domain in this case will not have restrictions, the range does and it is based on the asymptote.

SP #2: Unit E Concept 7: Graphing Polynomials

This problem is on Graphing Polynomials, and how to do so. Including x-intercept, y-intercept, zeroes (with Multiplicities), and end behavior. One thing to know is that all polynomials will be factorable.

The Viewer needs to pay special attention to the multiplicities, and how they work out in order to understand. A multiplicity of 1 would cause the line to go straight through, a even multiplicity causes a bounce off the x intercept not actually crossing it. A odd multiplicity would cause a curve through the graph.

SP# 1: Unit E Concept 1: Identifying x-intercepts, y-intercepts,vertex (max/min), axis of quadratics and graphing them. Quadratics in standard form.

   This problem involves the process of solving a quadratic by using completing the square, in order to get it in parent function form. And from there you would be able to solve for the vertex, y-intercept, axis (line of symmetry), and the x intercepts.

   The viewers need to pay special attention to every step taken in order to fully understand the concept. For example they must keep in mind that when finding the y-intercept its easier to get the answer when plugging in zero into the original equation (standard -form).