on the unit circle, where 0 < θ≤2π, when is tan θ undefined?\nθ = π and θ = 2π\nsin θ = cos θ\nθ = π/2 and θ…
on the unit circle, where 0 < θ≤2π, when is tan θ undefined?\nθ = π and θ = 2π\nsin θ = cos θ\nθ = π/2 and θ = 3π/2\nsin θ = 1/cos θ
Answer
Explanation:
Step1: Recall tangent - sine - cosine relation
The tangent function is defined as $\tan\theta=\frac{\sin\theta}{\cos\theta}$. A fraction is undefined when the denominator is equal to 0.
Step2: Find when cosine is 0
We set $\cos\theta = 0$. In the interval $0<\theta\leq2\pi$, $\cos\theta = 0$ when $\theta=\frac{\pi}{2}$ and $\theta=\frac{3\pi}{2}$.
Answer:
C. $\theta=\frac{\pi}{2}$ and $\theta=\frac{3\pi}{2}$