Unit T Big Question #4

Why do sine and cosine NOT have asymptotes, but the other four trig graphs do?

Watch this video to find out why! :]

Unit T Big Question #3

Why is a "normal" tangent graph uphill, but a "normal" cotangent graph downhill?

Watch this video to find out why! :)

Unit T Big Question #2

How do the graphs of sine and cosine relate to each of the others? (tangent, cotangent, secant, cosecant)

This video will go over how sine and cosine graphs relate to tangent and cotangent graphs.

Concept 1: Sine graphs relate to cosecant graphs because cosecant is the RECIPROCAL of sine. (sin=1/csc vice versa csc=1/sin) So, if sine equals 0, then cosecant is undefined. (1/0) This means that there will be a vertical asymptote where sine is 0.
Here is a picture that will help in further explaining this first concept:

Concept 2: Now that we can see what the asymptotes look like, the next part is that wherever sine reaches a maximum value of 1, cosecant will reach its minimum value of 1. And wherever sine reaches a minimum value of -1, cosecant will reach its maximum value of -1. (Purple Math)
Now lets look at this same photo but with the points marking 1 and -1:

Following the ideas learned in the second concept, lets apply what we know and fill in the graph:
(Cosecant kind of looks like a mirror image of sine)

Concept 3: Cosine graphs relate to secant graphs because secant is the RECIPROCAL of cosine. (cos=1/sec vice versa sec=1/cos) So, if cosine equals 0, then secant is undefined. (1/0) This means that there will be a vertical asymptote where cosine is 0.
Using these same ideas mentioned in concept 2, we can draw a cosine graph and use it to guide in making a secant graph. Look below:

This website will help understand why and how sine and cosine relate to secant and cosecant graphs.

http://www.purplemath.com/modules/triggrph3.htm

Citations:
http://www.purplemath.com/modules/triggrph3.htm
Mrs. Kirch's lecture on friday about all of the graphs

Unit T Big Question #1

How do the trig graphs relate to the Unit Circle?

a. Why is the period for sine and cosine 2π, where as the period for tangent and cotangent is π?

b. 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?

Studen Video #5: Unit S Concept 7: Assessment #4: Problem #5

What is this video about?
This video is about solving equations with half-angle formulas. We are given a problem that incorporates the use of half-angle formulas along with previous concepts learned in order to solve the entire problem. This video will go over step-by-step how to solve these kinds of problems.

What does the viewer need to pay special attention to in order to understand the concept?
The viewer needs to pay special attention to plugging in the correct formula. Also pay attention to the end when we determine the three answers. You must know your Unit Circle!

Unit S Concept 4: Student Problem: Assessment #2 (Parts 1-5)

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Student Video #4: Unit S: Concept 3: Assessment 3: #5

What is this video about?
This video covers #5 in the SSS packet from Unit S Concept 3: Using power-reducing formulas
It will go over, step-by-step, the process of solving #5 with the formulas given. We will also be using previous skills learned in algebra and previous units (half, double angles).

What does the viewer need to pay special to in order to understand the concept?
The viewer must pay attention to carefully plug in the correct power-reducing formula with the right positive/negative signs. Also pay attention to the distribution of the negative sign in one of the steps. The last thing to pay attention to is the denominator and how to get rid of it using reciprocals.