BQ# 3: Unit T Concepts 1-3

How do the graphs of sine and cosine relate to each trig graph?

Sine will be in Green.
Cosine will be in Orange.
Tangent will be in Blue.
Cotangent will be Yellow.
Cosecant will be in Pink.
Secant will be in Purple.

Tangent:

To see where the tangent graph will be we must first know about it's ratio. Tangent's ratio is y/x or sin/cos, cosine will determine where tangent will be. Where sine and cosine are both positive or negative then tangent will just be positive. If one of them is negative then tangent is negative. Tangent's asymptotes is determined by cosine, if cosine is 0 on the x-axis then that is one of tangent's asymptote. 

 Cotangent:

It's almost the same thing for cotangent except that it's sine that needs to be 0. If both sine and cosine are positive or negative then cotangent will be positive. If one of them is negative then cotangent is negative. The reason why cotangent is downhill is because of the asymptotes and where they are found. Since it has to be positive in quadrant 1, the cotangent graph has to be above the x-axis. Same thing for quadrant 2 but it's negative so it's below the x-axis.

Cosecant:

Where sine is 0, the asymptotes for secant will be those points. If sine is positive in two quadrants then cosecant will be positive, if it's negative, like in quadrants 3 and 4, then it's negative. Cosecant relates to the graphs by it's shape, the shape is between two asymptotes. So the asymptotes basically determine the shape and the asymptotes is where sine is 0.

 Secant:

Where cosine is 0 the asymptotes of secant can be found. The way the secant graph looks like, positive or negative, is the same as the cosine graph. The shape  of is is also determined by the location of the asymptotes and the cosine graph.