How do the trig graphs relate to the Unit Circle?
When you straighten out the unit circle, it is easier to decipher how it is related to trig graphs. With our former knowledge of trig functions, we know that each trig function has its positive and negative values, depending on which quadrant it is located in. According to ASTC, we know that sine is positive in the first and second quadrant and negative in the third and fourth(+ + - -). We can take what we know from the unit circle and use it to help graph our trig functions by even using the points on the unit circle ( 0, pi/2, pi, 3pi/2, 2pi). Because sin is positive in the first and second quadrant, this part of the graph will be above the x-axis (the distance from 0-pi). Likewise, the part of the unit circle in the third and fourth quadrant will be in the negatives, below the x-axis(the distance from pi-2pi). Similarly to the unit circle, trig graphs can also be divided into "quadrants". For Cosine, it is positive in the first and fourth quadrant and negative in the second and third quadrant(+ - - +). As a result, when a cosine graph is plotted, it will be above the x-axis for the first quadrant, below the x-axis for quadrant 2 and 3 because it is negative. Then it rises above the x-axis again when it enters quadrant 4. for Tangent/Cotangent, it is positive in the 1st, negative in the 2nd, positive in the 3rd, and negative in the 4th. The pattern is basically + - + -. So when graphing , quadrant 1 and 3 will be above the x-axis while 2 and 4 will be below.
Please Refer to this picture as you read through the text to help clarify on what I mean by the Quadrants and how it ultimately affects the graph. Additionally, a sketch of a sin, cos, and tan graph are provided in relation to the quadrants.