yysecx3Solution We know that for the equation y acotbx c t

Solution

We know that for the equation, y = a*cot(bx + c), the period is p/|b|. However, for y = a*sec(bx + c) and y = a*csc(bx + c), the period is 2p/|b|. Since b = 1/3 for all of these we see that the period of cot(x/3) is: p/|b| = p/|1/3| = p/(1/3) = 3p. Then, the period of both y = sec(x/3) and y = csc(x/3) is: 2p/|b| = 2p/|1/3| = 2p/(1/3) = 6p. I hope this helps!