The periods of all graphs, except for tangent and cotangent, are equal to 2π.
Whereas tangent and cotangent are equal to just π
Tangent's period is π because tangent(Θ) on the unit circle is = y/x = -y/-x = tangent(Θ + π)
Amplitudes are the same for everything, but sine and cosine, which is from ∞
Whereas sine and cosine are equal to 1
Comparing Sine and Cosine
Cosine is sine shifted left by π/2
Whereas sine is cosine shifted right by π/2
Vertical Asymptotes: Where and Why
Vertical asymptote of Tangent is where Cosine(Θ) = 0
Because Tangent = Sine/Cosine and cant divide by 0
Vertical asymptote of Secant is where Cosine(Θ) = 0
Because Secant = 1/Cosine and cant divide by 0
Vertical asymptote of Cosecant is where Sine(Θ) = 0
Because Cosecant = 1/Sine and cant divide by 0
Vertical asymptote of Cotangent is where Tangent(Θ) = 0
Because Cotangent = 1/Tangent and cant divide by zero
Google Sheets vs. Undefined Values
Instead of graphing by hand using calculators, I was able to use the Google Sheets program and be able to utilize its Auto-fill and Formula tools in order to decrease the time of creating the Tables of Values, from a full weekend to a matter of a class period.
This, unfortunately, did not come without hiccups. Similar to the graphing capabilities of a Ti-83 calculator, the logic behind Sheets' could not handle Undefined values, thus flipping the sign of every other asymptote. An anomaly is demonstrated when comparing the raw data(colored) and the function(black) on the graph.
Although pictures of the Table and Graphs were requested, I have decided it would be easier for both parties that they should rather be linked, since they were already online and the Graph was neatly organized and interactive.
Both URLs were also shorted by goo.gl since naturally they were extremely long.
http://goo.gl/ipbL3I - Table of Values
http://goo.gl/iqdmbO - Graphs
Both URLs were also shorted by goo.gl since naturally they were extremely long.
http://goo.gl/ipbL3I - Table of Values
http://goo.gl/iqdmbO - Graphs