Throughout this unit we not only reviewed trig but also learned new lessons. SOH CAH TOA can be rewritten as sin y/r, cos x/r and tan y/x.
we learned reference angles, which I find are easiest to solve when using a visual, such as a graph. The reference angle is determined by the closet x-axis, this will help decide whether or not you add or subtract from the degree of each quadrant.
we also learned the 2 special triangles. one we got by cutting a square in half and the other by cutting an equilateral triangle in half, these are used when we are asked for an exact ratio.
lastly we learned 2 new formulas, sin law and cosine law, these are used to solve non-right angle triangles, one or the other can only be used by fitting certain requirements
This week we learned how to multiply ugly fractions, which is almost exactly the same as what we were taught around middle school except with a few more extra steps. For this question factoring any numerator or denominator possible will help simplify the question. In the second line we noticed that there were matching terms on the numerator and denominator, and by following the rules of fractions anything over itself is equal to 1, because there’s no point to multiplying by 1 we’re able to just cross out the matching terms leaving us with what ever is left over as our simplified fraction.
This week we learned how to simplify “ugly” fractions. These are basically fractions that will involve factoring. A way to make these questions simpler is by crossing out common factors in the denominator and numerator of the fraction. The rule that anything divided by itself is equivalent to 1 still applies to these fraction, with that being said, by crossing out the common factors on the top and bottom of the fraction it shortens the question to it’s simplest form. We also learned that it is important to know the non-permissible values of x in the denominator. It is important to know because our denominator can never equal 0. therefore the non-permissible values of this expression are -5 and -8.
This week he learned how to graph reciprocal quadratic functions. When beginning these questions it is always easiest to start by graphing the original equation, in this example it is x squared minus 3. After graphing this draw a broken vertical line on the zeros or x-intercepts, because this graph has 2 solutions it will have 3 hyperbolas. The 2 “L” shaped hyperbolas hover right above the x-axis and almost touching the broken lines. The hyperbola on the bottom follows the same rules except it’s on the other side of the broken line.
This week in precalc we learned how to solve 2 inequalities by combining the equations. this only works when the equations have 2 variables. An important part of this process is when you send one equation to the other side of the equal sign, that they’re being added or subtracted properly or else the whole process will be ruined as the zeros will not be equal.
This week we learned how to solve for quadratic inequalities. When solving for these equations, factoring will be a key point as it gives the zero values. I like using the number line as a visual to find whether or not test numbers would give negative or positive results. Although this method is somewhat time consuming, it shows a simple, step by step way of solving.
This week because the midterm is coming up, we spent the week reviewing in preparation. I mostly went over reviewing ideas from chapter 1. Finding the difference is something critical because “d” is a variable used in almost every formula used for sequences and series, this is the same for the second idea I reviewed where instead I have to find “n”. With the third idea, using the quadratic formula, is another way of factoring. This is important because factoring was not only needed in chapter 3, but a concept needed for the future chapters. knowing how to use the quadratic formula is also critical since knowing this formula can also be used to find the discriminate.
This week we learned how to model using quadratic functions. This is a question I struggled with mostly because I didn’t quite understand the question. I found this question easier to solve when key words are pulled out of the question. In this question the words sum, 20cm, produce, and area were important to keep in mind when solving this. I got the initial equation W+L =20cm because the question asked for the sum. Next I moved the W to the other side on the equal sign, giving me the value of L. Area is found by LxW so all that was left was multiplying by W to get the area; although, in this question W was not provided so the final equation is written area= W(20-W)
This week we learned three different formulas used to help graph. Each of these graph are important because they supply us each with different information used for plotting. To fully graph an equation its important to have all our information and by doing so we need to be able to change from one formula to another. Although we learned how to complete squares in our past units, I found this most difficult in this unit too but at the same time this concept is very important since when doing so it gives us standard form. Standard in my opinion is the best form because it gives us the vertex and line of symmetry. When in standard form, convert into other forms seems easier.
This week in Precalc we learned how to plot the vertex using an expression. I found it is easier to solve this using a graph. substitute X for numbers between -3 to 3 then solve for Y and fill in the graph. as you can see on the graph and parabola the plot (2,-3) is the lowest point of the graph making it the vertex