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Welcome to William's Math Analysis Blog

## Tuesday, April 22, 2014

### BQ#4 – Unit T Concept 3

`The way that a tangent and a cotangent graph go has to do a lot with the asymptotes. The position of the asymptote describes where the graph has to go. You also have to take into account how the way that the sign of the graph has been determined already. For that reason the "normal" tangent graph goes uphill and the "normal" tangent graph goes downhill. `

### BQ#3 – Unit T Concepts 1-3

`These two graphs when seen without a background the graphs look just the same. What differs these two are where the graph starts. Other than that the graphs are very similar. Both of them have two parts in the negative section and two in the positive one. The period for both of these are 2pi. They both have amplitude, for that reason, these two typed of graphs are very similar.`

## Thursday, April 17, 2014

### BQ#5 – Unit T Concepts 1-3: Asymptotes

Why do sine and cosine NOT have asymptotes, but the other four trig graphs do? Use unit circle ratios to explain.
First of all, we should be familiar that asymptotes happen whenever we get undefined. The only way to get undefined is to be divided by zero. If we refer to the circle ratios of sine and cosine the ratios would be sin=y/r and cos=x/r. We know that r will always equal one so there is no way that sine and cosine will randomly appear with a zero on the bottom. However, every other trig ratio have some value in which the bottom can equal zero, making it possible for them to have an asymptote.

## Wednesday, April 16, 2014

### BQ#2 – Unit T Concept Intro: How do the trig graphs relate to the Unit Circle?

Period? - Why is the period for sine and cosine 2pi, whereas the period for tangent and cotangent is pi?
The reason why sine and cosine have a period of 2pi is because that's how long it takes for a sine/cosine graph to repeat itself. The repetitions are based on the signs of the trig function and the unit circle. Whereas tangent, tangent repeats the sign pattern in the unit circle, so for it to complete a repeated cycle. So in 2pi there would be 2 graphs looking exactly the same for that reason only 1 pi is needed for the graph.

Amplitude? – How does the fact that sine and cosine have amplitudes of one (and the other trig functions don’t have amplitudes) relate to what we know about the Unit Circle?
We have to remember that in the unit circle, a value greater than 1 and less than -1 would result as an error, because the values cannot be greater than that on the unit circle. for that reason those are used as amplitudes while graphing a sine/cosine graph.

Works Cited
http://edunettech.blogspot.com/2013/10/the-graphs-of-six-trigonometric.html

## Thursday, April 3, 2014

### Reflection# 1: Unit Q, Trigonometric Identities

What does it actually mean to verify a trig identity?
When we are asked to verify an identity what we have to do is make sure that both sides equal each other exactly. we can do this by substituting trig functions with each other. No matter what, both sides equal the same thing. we just have to check that its true.
What tips and tricks have you found helpful?
Well the best tip for this unit is memorize the identities. If you know your identities you can look at a problem and be ahead of the problem. There were times where i knew what i was going to do in the problem two steps before i actually did them. This was thanks to me memorizing the identities.
Explain your thought process and steps you take in verifying a trig identity.  Do not use a specific example, but speak in general terms of what you would do no matter what they give you.
The first thing that i would see is what are the terms in which we have to end up with. Is it going to be a fraction? Do they cancel at the end? these are some questions that go through my mind in the beginning. then if i have a fraction i try to get rid of the bottom part if possible. then i try to set everything to sin and cosine. so that later i can just move those two around to turn them into the trig function it has to equal to.