Question

on the unit circle, where 0 < θ ≤ 2π, when is tan θ undefined?
θ = π and θ = 2π
sin θ = cos θ
θ = π/2 and θ = 3π/2
θ = 1/cos θ

Explanation:

Step1: Recall tangent - cosine relation

Recall that $\tan\theta=\frac{\sin\theta}{\cos\theta}$. A fraction is undefined when the denominator is zero.

Step2: Find when cosine is zero

We want to find when $\cos\theta = 0$ for $0<\theta\leq2\pi$. In the unit - circle, $\cos\theta$ is the $x$ - coordinate of the point on the unit - circle corresponding to the angle $\theta$. The values of $\theta$ for which $\cos\theta = 0$ and $0<\theta\leq2\pi$ are $\theta=\frac{\pi}{2}$ and $\theta=\frac{3\pi}{2}$.

Answer:

$\theta=\frac{\pi}{2}$ and $\theta=\frac{3\pi}{2}$