Big Questions Blog Post #1

The BIG Question:

1. How do the trig graphs relate to the Unit Circle?
A Period: Why is the period for sine and cosine 2pi whereas the period for tangent and cotangent is pi?
Periods are cyclical, they are referring to revolutions of the unit circle. A period is only one time around the trig graph (one revolution around the unit circle).




This cycle repeats until the end of time, that's why it is called a cyclical graph. The difference between the periods of sine/cosine and tangent/cotangent is accredited to ASTC. Sine's order is positive positive negative negative. The signs repeat at 2pi. Now if we look at tangent, the ASTC is positive minus positive minus. For this, we only have to go to pi to allow the pattern to repeat itself.


B) Amplitude: 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?

(This is our friend)


Amplitudes are found when sine is pi/2 and 3pi/2, which are the quadrant angles of 90 degrees and 270degrees. Cosine is similar, however this occurs at zero degrees, pi, and 2pi.

The rest of the trigonometric functions (tangent, secant, cosecant, cotangent) are similar. They have asymptotes when the denominator of the ratio is zero (this makes it undefined and it cannot occur).



google images used.