Find all solutions

$\displaystyle sec^5\theta=4sec\theta$

Are you suppose to let this equal to 0, but I thought thats only for quadratics? and it would not be a quadratic?

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- Mar 10th 2010, 06:29 AMpurplec16Solutions
Find all solutions

$\displaystyle sec^5\theta=4sec\theta$

Are you suppose to let this equal to 0, but I thought thats only for quadratics? and it would not be a quadratic? - Mar 10th 2010, 08:28 AMhollywood
It's a degree-5 equation, but no need to fear:

$\displaystyle sec^5\theta-4sec\theta=0$

$\displaystyle (sec\theta)(sec^4\theta-4)=0$

$\displaystyle (sec\theta)(sec^2\theta+2)(sec^2\theta-2)=0$

The middle one can't be zero, so you'll get one family of solutions from the first one and two families of solutions from the second. They'll be families of solutions because if $\displaystyle \theta$ is a solution, then $\displaystyle \theta+2n\pi$ is a solution for all integers n.

Post again if you're still having trouble.