BQ #3: How do the graphs of sine and cosine relate to eatch of the others?

Sine and Cosine relates to Tangent whenever Cosine/X is equal to zero. It happens to be where the curve on the graph is at. The curve is based on the ASTC of Tangent. Therefore, it will have different curves depending on the ASTC.

Cotangent will have an asymptote whenever sine is equal to zero. When sine is equal to zero, you will have undefined answer, therefore have an asymptote. The graph is uphill/downhill depending on where the asymptote is placed at. In this situtation, asymptote is located at 0, Pi, and 2pi.

Secant is the reciprocal of cosine. Secant will have an asymptote whenever cosine is equal to zero. The asymptote will be at pi/2, 3pi/2. On the first curve, it goes up next to the asymptote because the recicprocal of a fraction will make the number big, therefore will have to increased the curve. The curve will touch the "mountain" based on ASTC however, it will never touch the asymptote.

Cosecant will have an asymptote whenever sine is equal to zero because cosecant is the reciprocal of sine. Sine is zero at 0, pi, 2pi. The curve will depend on the ASTC of Sine. Sine is positive in qudrant 1,2. Because of that, the graph will be above the x asix. In qudrant 3,4 sine is negative. The graph will be below the x axix and will get close to the asymptote.