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in this question were trying to match each of these graphs that are given with its corresponding equation now the most useful thing to keep in mind here is that when you see a cosine and a sine pair that is J in a parametric equation thats generally going to give you rotation and that goes back to the idea that on a circle if we imagine T being sort of like the angle that the coordinates of a point on a circle would be cosine T and sine T right so the when we have a cosine and a sine pair in an equation it suggests to us rotation so and youll notice we see lots of cosine and sine pairs here keep in mind also that if you have something multiplying in front of the cosine and sine thats going to act like a radius so if I look at my equations here I notice that you know these this one this one and this one all have a cosine and sine pair that dont have a radius on them right so the radius isnt changing radius would be constant at one whereas the one on the top here and the one on th