solve on the interval 0 2pi
4 sec x+6=-2
The solution to the problem is as follows:
4secx + 6 = −2
⟹secx = −2 = sec π/3
⟹x = 2nπ ± π / 3, n∈W
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
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:
\(x = \frac{2 \pi}{3} , \frac{4 \pi}{3}\)