Unit U BQ 6

1. What is continuity? What is discontinuity ?
 A continuity is when you can draw a graph with out and holes, jumps, unbounded behavior like shown in the second picture.
A discontinuity is when you have a graph with jumps , holes, or unbounded behavior. Like in the first picture it is s jump with holes.

2 What is a limit? When does a limit exist? when does a limit not exist? what is the difference between a value and limit ?
A limit is when you plug in x in to the equation.
A limit exist when two things have the same point.
A limit does not exist when they end up at different points like picture 1
A limit is not always on the graph but its what you expect. a value is what your really looking for.

3 How do we evaluate limits numerically, graphically, and algebraically ?
solving limits numerically is very easy. first you need to draw a table with 14 squares in two rows. on the top 7 rows you want to write down the values that you will be plug in to the equation.to find the answers.so solve it graphically we want to the limits. so we look at the graph and determan where everything is by looking at the points and derection of the graph. To solve it algebraically you have three ways of finding them. first is the substitution method witch is when you plug in 0 and see what you get. you can eather get a number , zero, undefined , there is also the factoring method witch simplifyes the equation and then use substitution method agian. and there is also the last one witch is conjugate is when you times it by the conjugate so it simplifies out.

BQ#3 unit t

how do the graphs of sine and cosine relate to each of the others ?
tangent is like an inverse of a sine and cosine.
cotangent it uses the base of sin and cosine but in this one it has two parts of the graph
secant it is when ever cosine equal to zero and it looks like a parabola
cosecant when ever sine is zero and it has two asymptotes

BQ#5 unit T concept 1-3

5 Why do sine and cosine not have asymptotes, but the other four graphs do?
Both sine & cosine cycle past the value 0, therefore secant & cosecant approach 1/0, which isn't allowed mathematically. It is at this value you will find the asymptotes.

BQ #4 unit t concept

3 Why is a "normal" tangent graph uphill, but a "normal" tangent down hill?
There are parts of a graph that will slope down but after it reaches the center it turns 180 degrees and goes to the opposite direction. its like the unit circle when open the the fan and that sewwt  lile

BQ #2 unit T

What is a period ?
A period is a set of repeating graphs

Why is the period for sin and cosine 2 pie ?
It is because when graphing it the quadrants are different in sin and cosine have the negative on the same side as the other negatives and some with positives. it needs to go threw one whole round of it for a graph to finish.

What is amplitude ?
it is what number that will determine how far your graph will go up.

Why does sin and cosine have amplitudes of 1?
as you see in the unite circle we see that sin and cosine both have the hypotenuse in its equation and on the unit circle that hypotenuse is always one no matter what.

Reflection #1- Unit Q :Verifying Trig Identities

1. To verify an Identity is to find what is giving using your rules or functions. You need to find each one by rules of other trigs to ether simplify them the most you can or in an equation to prove it out. There are many ways you can solve for a trig function. Not all the steps are right so  you can have your own way of doing it.

2.some tricks that i have are not really help full to most people but it helps me. I always look for anything that can be substituted.I look at old examples to see the procces and then i apply it. I also like to make the problem as simple as possible so that it wont confuse me.

3. These equations can be solved in so many ways. The steps i use in solving the equation start out with me looking at it and seeing if i can simplify it. the i look at each of the trigs and see if they are the same or not. After i look at that i see if any of them can be substituted to make them all match. After i do all that i just go with the flow and solve them by step by step. at the end i make sure my work is correct then move to the next problem.

SP7: unit Q concept 2 identities

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