Excellent work. One important error: the periods of the secant and cosecant are both 2 pi, not pi. Each graph has a repeated pattern consisting of a positive segment of length pi followed by a negative segment of length pi. The values don't start repeating until we return to the positive segment again--both segments are required to complete the period. Another way of putting it is that we have to go from a positive vertical asymptote to another positive vertical asymptote, then to the negative vertical asymptote and to another, before we again get to a positive vertical asymptote. In contrast the tangent function repeats all its values in over a horizontal segment of length pi, starting from negative vertical asymptote and going to the positive then immediately returning to the negative asymptote and starting all over again. Your error spanned only a small part of one problem and didn't cost you many points; your graphs were all correct on this problem. You just misinterpreted those two periods. I thought you had made a common error on #6 but in explaining it here I realized you were right. That increases your grade from the 90% I originally posted to 95%. You also lost a couple of points on the arc distance problem. On a circle of radius 10 the arc distance corresponding to 15 radians is (10 units / radian) * (15 radians) = 150 units of distance. You correctly found the arc distance from the positive x axis to the final point of the arc, but the arc does complete the two complete circles as well before it finishes this last segment, and this distance counts. For example if the arc represented the path of a particle in a force field the work done against that field on the entire arc would certainly count.