# Solve a Trig Equation Containing secant

1. Nov 13, 2013

### nickb145

1. The problem statement, all variables and given/known data

sec(5x)-5=0
2. Relevant equations

3. The attempt at a solution

I turned it into 1/cos(5x)=5 x=θ/5
then i switched it to cos(5x)=/1/5

Then cos-1(1/5)=θ which = 1.36 (one solution) then divided by 5 which is .2738 which works as one solution
since the positive cos is in the 1st and 4th quadrant i need to subtract 2pi to 1.36= 4.91 then divide by 5 which gives me .9827 which also works

But i am stuck after that

Last edited: Nov 13, 2013
2. Nov 13, 2013

### Staff: Mentor

You could also say that cos(5x + k*2$\pi$) = 1/5, and since cosine is positive in Q IV, you could also say that cos(-5x + k*2$\pi$) = 1/5, where k is an integer.