on the unit circle, where 0 < θ≤2π, when is tan θ undefined?\nθ = π and θ = 2π\nsin θ = cos θ\nθ =…

on the unit circle, where 0 < θ≤2π, when is tan θ undefined?\nθ = π and θ = 2π\nsin θ = cos θ\nθ = \\frac{π}{2} and θ = \\frac{3π}{2}\nsin θ = \\frac{1}{cos θ}

on the unit circle, where 0 < θ≤2π, when is tan θ undefined?\nθ = π and θ = 2π\nsin θ = cos θ\nθ = \\frac{π}{2} and θ = \\frac{3π}{2}\nsin θ = \\frac{1}{cos θ}

Answer

Explanation:

Step1: Recall tangent - sine - cosine relation

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

Step2: Find when cosine is zero

We need to find when $\cos\theta = 0$ for $0<\theta\leq2\pi$. In the unit - circle, $\cos\theta = 0$ when $\theta=\frac{\pi}{2}$ and $\theta=\frac{3\pi}{2}$.

Answer:

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