Solve the equation. (Enter your answers as a comma-separated list. Use n as an arbitrary integer. Enter your response in radians.) sec2(x) + 5 sec(x) − 14 = 0

Question

Solve the equation. (Enter your answers as a comma-separated list. Use n as an arbitrary integer. Enter your response in radians.)

sec²(x) + 5 sec(x) − 14 = 0 

x=

Answer 1

First change the variable as: y = sec(x).

Therefore: y² + 5y -14=0 .

This can be decomposed as: (y-2)(y+7)=0, which means y = 2 or y=-7.

Now x = arcsec(y), and so: x = arcsec(2) = 60^o = 1.047 radians, or x=arcsec(-7) = 98.21⁰ = 1.71 radians.