Trig Secant problem

[gkagawa]

4. Determine the approximate solution of secx - 5 = 0 in the interval x E {0,2pi] to the nearest
hundredth of a radian.

I tried to enter it in my calculator as sec[sup:27aedypg]-1[/sup:27aedypg]5 but I got an error message. I looked at a graph of sec x and I can see that there are 2 values where y=5 in the given interval, but how do I calculate it?

 

[BigGlenntheHeavy]

\(\displaystyle sec(x)-5 \ = \ 0, \ 0 \ \le \ x \ \le \ 2\pi\)

\(\displaystyle sec(x) \ = \ 5, \ \frac{1}{cos(x)} \ = \ 5, \ cos(x) \ = \ \frac{1}{5}\)

\(\displaystyle x \ = \ arccos(1/5) \ \dot= \ 1.369438406 \ or \ x \ \dot= \ 2\pi-1.369438406 \ \dot= \ 4.91374690118.\)

 

[gkagawa]

Thanks for the answer!