find all solutions

Question

Find all solutions of sec(x−5)=2sqrt3/3.

x= 

(Leave your answers in exact form and enter them as a comma-separated list. Your answer should involve k, where k is an integer.)

Test values of k to find all solutions on the interval [6π,8π].

x= 

(Leave your answers in exact form and enter them as a comma-separated list.)

Answer 1

have

x=cos^-1((√3)/2)+5+2k*pi

also have

x=(-)cos((√3)/2)+5+2k*pi

when k =3 then 6*pi is added to each x

and 5 radians is approx. 1.6*pi

k=3 should have both x in range requested

Answer 2

Convert sec (x - 5) to 1 / (cos (x - 5)) and solve.