Me Gusta Math Analysis : April 2014

Tuesday, April 22, 2014

BQ#4 - Unit T Concept 3

Tangent goes uphill because its positive in quadrants one and three and negative in quadrants two and four. Its positive in zero uphill and pi uphill etc. The asymptotes are in zero, pi/2, pi, 3pi/2 and 2pi because x is zero. The tangent graph starts at negative and goes uphill to be positive and to go to the next quadrant.
Cotangent goes downhill because its postive in quadrants one and three and negative in quadrants two and four, just like tangent. Its negative downhill pi/2 and 3pi/2 etc. The asymptotes are in zero, pi, and 2pi because y is zero. The cotangent graph starts positive and goes downhill to be negative its like the reciprocal of tangent.

Monday, April 21, 2014

BQ#3 - Unit T Concepts 1-3

First of all sine and cosine dont have asymptotes when the other graphs do have asymptotes. Tangent related to cosine when cosine is zero because it becomes undefined and the asymptote are in pi/2 and 3pi/2. For cotangent related to sine when sine is zero because it becomes undefined and the asymptotes are in 0 and pi. For secant when cosine is zero then secant is undefined so there's going to be asymptotes at pi/2 and repeat every pi unit. Finally for cosecant when sine is zero then cosecant is undefined like secant, so there's asymptotes at pi and continue every pi unit.

BQ#5 - Unit T Concepts 1-3

The reason for sine and cosine not having asymptotes is because r equals 1 that makes them undefined. Sine is y/r=1 and cosine is x/r=1, there needs to be a zero at the denominator to have asymptotes. Unlike tangent(y/x) and secant(r/x) have asymptotes at 90 and 270 degrees because that's where x=0. Cosecant(r/y) and cotangent(x/y) that have asymptotes at 0 and 180 degrees because that's where y=0.

Wednesday, April 16, 2014

BQ#2 - Unit T Intro

The quadrants from the unit circle, when placed horizontally in numerical order, create the basis for the trigonometric graphs. Since sine is positive in quadrants A and S and negative in quadrants T and C, when unwrapping it starts positive and positive then negative and negative and start again in another revolution. For cosecant its positive in quadrants A and C and negative in quadrants S and T, when unwrapping it starts at positive then negative then negative and end positive. That's how trig functions relate to the unit circle.

The reason sine and cosine is 2pi because it needs all four quadrants to repeat unlike tangent and cotangent needs only half that why it's just pi.

Sine and cosine has an amplitude of 1 because it can only be between -1 to 1 unlike the others there's no limit so their amplitude can greater than 1.

Friday, April 4, 2014

Reflection #1 - Unit Q: Verifying Trig Identities

What does it actually mean to verify a trig identity?

To solve for a trig identity the answer has to be true no matter what beacuse one side of the equation has to match the other side. To do that several steps has to be made. In a regular equation you can work on both sides but in an identity you can't because it won't prove the identity to be true.

What tips and tricks have you found helpful?

Knowing the three types of identities help to verify the equation. The unit circle came in handy too because we had to see were it landed in the unit circle. For concept 4, its easy to plug in equation ones it's verify, to see were it lands.

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.
When solving an identity i look to see if there's any identities or if can be split apart. From there I see how can manipulate the equation to verify it. There are so many ways to verify its like a puzzle. Ones i see the end of the equation i start to verify to get my answer.