Question

Over an interval [-2π, 2π] state the values for which the secant function is not defined.

Answer 1

Where is the cos = 0?

Answer 2

Since the secant is 1/cosine, and since undefined means here that one cannot have a zero in the denominator, look for where the cosine equals zero in this interval. And since the interval is -2pi to 0 and then 0 to 2 pi, you are "going around the circle" twice, that is, you start at zero and "back up" to -2pi. That is your starting point. You go once around the circle to get back to 0, and then go once more around the circle to get to 2pi. Look for 4 values at which the cosine equals zero.

Answer 3

Last hint. Think vertical, up and down. Any more than that, and I would just be giving you the answer.

Answer 4

\[\sec(x) = \frac{1}{\cos(x)} \]

As stated before, where is cos(x) = 0?