BQ#2: Unit T Concept Intro

A)   When you think about sine and cosine, we have to remember their periods are 2pi and it's like that due to their similarity to the Unit Circle.



In the Unit circle Sine is positive in the first and second quadrant and negative in the third and fourth quadrant. If we start from zero and do one complete rotation to get it to be positive again, then that is a 360 degree or 2pi rotation. So when we stretch the Unit Circle into a line, the cycles will be stretched out too because the first two quadrants will be above the x-axis and the last two will be below the x-axis. 

 

 

 





This also applies for cosine since quadrant I and IV are positive and quadrant II and III are negative. We need to start at 0 degrees and as we move around in the Unit Circle well reach the positive when we get to 360 degrees. When it reaches 360 degrees the it made one complete rotation. If we again stretch out the Unit Circle to a straight line for cosine then we will start above the x-axis since quad. I is positive and for quads II and III it will be below the x-axis. As we approach quad IV to make a cyclical then it go back up above the x-axis.

 

Tangent is different because it's only half the trip to get a cyclical. Quadrants I is positive and quadrant II is a negative so we already have our cyclical. On the Unit Circle, it will start at 0 degrees and when we reach a positive again it will be at 180 degrees and the radian value is pi.