BQ#4 – Unit T Concept 3

"Normal" Tangent & "Normal" Cotangent Graph❤︎☁︎☀︎

Tangent☽

Each space between the asymptotes is a quadrant from the unit circle. tangent equals sine over cosine and tangent is positive in the first and third quadrant and also negative in the second and fourth quadrant. the graph has to be uphill down to up because the graphs cannot touch the asymptotes. there are asymptotes where "x" is equal to 0. 

Cotangent❀

For Cotangent its the reciprocal of the tangent graph. the asymptotes determine how the graph will look. There are boundaries in both graphs these graphs cannot touch the asymptotes. cotangent equals cosine over sine. asymptotes will be graphed where "y" is equal to 0. We start by graphing close to the asymptote and end below the graph.

BQ#3 – Unit T Concepts 1-3

   (All Asymptotes are based on Sine & Cosine☀︎)

Tangent, Cotangent, Secant & Cosecant ❤︎

All Asymptotes are based on sine and cosine. Asymptotes for these graphs occur when cosine is equal to 0. tangent has an asymptote where cosine is equal to 0 because of the ratio y/x this will end up being undefined. All these four trig graphs contain sine and cosine. These graphs consist of repeating units. Each period is repeated in a negative and positive manner. The tangent graph is positive and the cotangent graph is negative, where as the cosecant and secant graphs can start or end in either positive or negative direction.

BQ#5 Unit T Concepts 1-3

Sine & Cosine 
These two trig graphs will never have asymptotes because the ratio for sin is y/r and the ratio for cosine is x/r. "r" will always equal 1 therefore this function will never be undefined.

Cosecant, Secant, Tangent & Cotangent
These functions may have asymptotes because of their ratios. csc=r/y, sec=r/x, tan=y/x & cot=x/y. We know that the "x" or "y" value could be 0 which will make anything divided by it an undefined graph. secant and tangent will have the same asymptotes because of the "x" value on the bottom of their rations. The same goes for cosecant and cotangent because the "y" value is in the denominator of both of them.

BQ#2 Unit T Concept Intro

Trig Graphs

• The trig graphs relate to the unit circle because they are repeating units due to the different quadrant values. (ASTC)
• Sine and cosine have a 4 part repeating unit whereas tangent and cotangent do not have repeating units. 
• we have amplitudes  because we have limits for sine & cosine we can only stay between (-1,1) its the lowest and highest that we can go in the unit circle.

Reflection#1-Unit Q: Verifying Trig Identities

Reflection

1. What verifying a trig function means is that we use either the ratio identities, the reciprocal identities or the pythagorean identities to simplify a ratio as much as we possible can. We must also look for a way to simplify it but in a way that isn't going to make the problem a bigger mess than it already might be. 

2. Tips i have found helpful are to do a lot of practice, memorizing all of the identities and also watching videos from other students not only the teachers because some teach it in a way that i better understand or they clarify something in a different way. Like in Concept 5 i was completely lost it took me a while but with all the practice and the videos I've re-watched it really helps to stay on task and to ask questions when you need to. 

3. The steps i take to solving a trig ratio are simple. I analyze the problem and try to figure out what would be the best way to approach it. I avoid making the trig ratio a big mess, i do not want to make it harder to solve. I also see and picture which identity i can use whether its the ratio identity, reciprocal identity, or the pythagorean identity. Then i look to solve and simplify it to the simplest answer i can simplify it to.