Wednesday, April 16, 2014

BQ#2: Uit T Concept Intro

The trig functions when graphed relate to the unit circle because when their values graphed and on the unit circle are the same there simple extended when there graphed.

Why is the period for sine and cosine 2pi, whereas the period for tangent and cotangent is pi?
It takes up to all four quadrants to repeat the same pattern. tangent and cotangent have a period of pi because they already have a positive and negative value on the first two quadrants. 
Sine and cosine can not be bigger than one because of their ratios. 

Friday, April 4, 2014

Reflection#1: Unit Q Concept 5: Verifying Trig Identities

1. What does it actually mean to verify a trig function?
It means to solve each side of the equation so that they are equal to each other. You are proving that the identity is always true.You must simplify one of the sides by  finding the GCF, substitution for an identity, multiplying by the conjugate, combining fractions with a binomial denominator, separating fractions with monomial denominators, or factoring as you break things down.The zero product property (ZPP) may apply which means your equation is equal to zero.

2. What tips and tricks have you found helpful?
The process of verifying trig functions a bit quicker when having the identities memorized so that you won't have to keep looking back and checking what they are. Another way to make things a bit easier is to be fully aware of what you are able to do with the trig functions such as, substituting an identity, multiplying by the conjugate, separating fractions with monomial denominators etc.Always try something even if you think your unsure of what to do. Once you start the problem you start to notice things that you can either cancel, substitute, factor etc.RRemember that you can never divide by a trig function.

3. Explain your thought process and steps you take in verifying a trig function. Do not use a specific example but speak in general terms in what you do no matter what they would live you. 
It is better to first work with the one side of the equation that is more complicated and then you can move onto the other. You must look if there is a GCF, substitution for an identity, you are able to multiply by the conjugate, combine fractions with a binomial denominator, separate fractions with monomial denominators, or factor. In order to fully solve you must continue to look for these opportunities. Keep in mind that you may convert some terms to sines and cosines but not all. You cannot touch the right side.There is not only a one way process however it is possible.