solve the equation for x, where x is restricted to the given interval. y = sec x - 8, for x in 0, pi/2) u…

solve the equation for x, where x is restricted to the given interval. y = sec x - 8, for x in 0, pi/2) u (pi/2, pi x = (use parentheses to clearly denote the argument of each function.)

solve the equation for x, where x is restricted to the given interval. y = sec x - 8, for x in 0, pi/2) u (pi/2, pi x = (use parentheses to clearly denote the argument of each function.)

Answer

Explanation:

Step1: Isolate sec x

Add 8 to both sides of the equation $y = \sec x-8$. $y + 8=\sec x$

Step2: Use inverse - secant function

Since $\sec x=y + 8$, and $x\in[0,\frac{\pi}{2})\cup(\frac{\pi}{2},\pi]$, the inverse - secant function $\text{arcsec}$ gives us the solution. $x=\text{arcsec}(y + 8)$

Answer:

$\text{arcsec}(y + 8)$