Why is hypotenuse always positive when dealing with soh cah toa in graphs?

By definition a2=b2+c2, so if b<0 or c<0 or both, b2 and c2 will (always) be positive, and so their sum will always be positive, therefore the hypotenuse, a, will always be positive.

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Period is the time it takes for one “cycle” to complete. in the parent sine function, period is 2*pi since sin(0) = 0, sin(pi/2) = 1, sin(pi) = 0, sin(3pi/2) = -1, and sin(2pi) = 0. at that point, the sequence repeats itself. i’m not sure if your graph is similar to the sine function since you didn’t provide a picture, but you can find the period by looking at a graph.