Question

Saved Find all solutions of 5−4 secx = −3 on the interval [0, 2π).

Answer 1

Uterlly useless considering 11-34 is 3

Answer 2

Answer:

$\theta=\dfrac{\pi }{3}\\\\\theta=\dfrac{5\pi }{3}$

Step-by-step explanation:

$\theta = x$

$5-4 \sec (\theta) = -3$

$-4 \sec (\theta) = -3-5$

$-4 \sec (\theta) = -8$

$\dfrac{-4 \sec (\theta)}{-4} =\dfrac{-8}{-4}$

$\sec (\theta)=2$

Once

$\sec(\theta)=\dfrac{1}{\cos(\theta)}$

$\sec (\theta)=2 \implies \dfrac{1}{\cos(\theta)}=2 \implies \cos(\theta)=\dfrac{1}{2}$

The solutions for $\cos(\theta)=\dfrac{1}{2}$ are

$\theta=\dfrac{\pi }{3}+2\pi n, n \in \mathbb{Z}\\\\\theta=\dfrac{5\pi }{3}+2\pi n, n \in \mathbb{Z}$

But once the interval for the solution was given,

For $[0, 2\pi)$

$\theta=\dfrac{\pi }{3}\\\\\theta=\dfrac{5\pi }{3}$