Question

Solve on the interval 0 2pi 4 sec x+6=-2

Answer 1

The solution to the problem is as follows:

4secx + 6 = −2

⟹secx = −2 = sec π/3

⟹x = 2nπ  ± π / 3, n∈W

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Answer 2

Answer:

$x = \frac{2 \pi}{3} , \frac{4 \pi}{3}$

Step-by-step explanation:

Given the equation:

$4 \sec x+6 = -2$

Subtract 6 from both sides we have;

$4 \sec x =-8$

Divide both sides by 4 we have;

$\sec x = -2$

We know that:

$\sec x = \frac{1}{\cos x}$

then;

$\cos x = -\frac{1}{2}$

⇒$x = \cos^{-1} (-\frac{1}{2})$

Since, cos is negative in quadrant IInd and IIIrd quadrant  

⇒$x = \pi -\frac{\pi}{3}, \pi +\frac{\pi}{3}$

⇒$x = \frac{2 \pi}{3} , \frac{4 \pi}{3}$

therefore, the value of x over the interval $[0, 2 \pi]$ are:

$x = \frac{2 \pi}{3} , \frac{4 \pi}{3}$