Sketch the graph of $y = \tan^2 x$ for $0 \leq x \leq 360$. - Edexcel - GCSE Maths - Question 11 - 2018 - Paper 3

The tangent function has vertical asymptotes at $x = 90^\circ$ and $x = 270^\circ$ within the given interval. At $x = 0, 180, 360$, $y = 0$ because $\tan^2(0) = 0$, $\tan^2(180) = 0$, and $\tan^2(360) = 0$. The function will approach infinity as $x$ approaches the asymptotes.

Beginning at the origin $(0,0)$, the graph will rise steeply toward positive infinity as we approach $x = 90^\circ$ from the left. At $x = 90^\circ$, there is a vertical asymptote. The function decreases back to zero as $x$ approaches $x = 180^\circ$, where $y = 0$ again. A similar pattern occurs from $180^\circ$ to $270^\circ$ with another vertical asymptote, and then rises back towards infinity as $x$ approaches $270^\circ$ from the left and falls back to zero at $360^\circ$.