Question

What are the key features of the graph of the tangent function?

Answer 1

Answer:

Tangent is sine over cosine. Since sine and cosine are periodic, then tangent has to be, as well.–π to –π/2: The tangent will be zero wherever its numerator (the sine) is zero. This happens at 0, π, 2π, 3π, etc, and at –π, –2π, –3π, etc. The tangent will be undefined wherever its denominator (the cosine) is zero. A zero in the denominator means you'll have a vertical asymptote. So the tangent will have vertical asymptotes wherever the cosine is zero.