BQ#3

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Tangent the picture graph on the top shows sine cosine and tangent. since tangent is y/x we know that x is cosine so we get asymptotes whenever the denominator = 0 so that means whenever cosine =0 there will be an asymptote. if one of sine or cosine is negative tangent will be negative
Cotangent is on the bottom of the picture. here we know that cotangent is the opposite tangent so the ratio is x/y so now whenever y=0 there will be an asymptote. but if sine and cos are positive the graph is going down hill if its negative it goes up.

secant is on the top picture as you can see wherever cosine =0 there you can find secant it looks like a parabola because there are asymptotes

 for cosecant It is the last picture as you can see it is the same as secant but you can find cosecant whever sine =0 and it too has asymptotes which give it its shape