Question

0° ≤ θ ≤ 180°. find the value of θ in degrees. sec(θ) = -1 write your answer in simplified, rationalized form. do not round. θ = °

Explanation:

Step1: Recall secant - cosine relationship

Since $\sec\theta=\frac{1}{\cos\theta}$, the equation $\sec\theta = - 1$ can be rewritten as $\frac{1}{\cos\theta}=-1$.

Step2: Solve for cosine

Cross - multiply to get $\cos\theta=-1$.

Step3: Find theta in given range

In the range $0^{\circ}\leq\theta\leq180^{\circ}$, when $\cos\theta = - 1$, $\theta = 180^{\circ}$.

Answer:

$180$