How many solutions does tan^2(x)-25=0 have on interval 0,2pi

i can get to tan(x)=5 but what then.

Question

How many solutions does tan^2(x)-25=0 have on interval 0,2pi

i can get to tan(x)=5 but what then.

jim_thompson5910 · Answer

keep in mind that if x^2 = 25 then x = 5 or x = -5

jim_thompson5910 · Answer

since (5)^2 = 25 and (-5)^2 = 25

jim_thompson5910 · Answer

that means you should have these two equations

tan(x) = 5  or tan(x) = -5

jim_thompson5910 · Answer

you then apply the arctan function to both sides for each equation to solve for x

anonymous · Answer

ok i did, 1.373400766945015860861271926445 and -1.373400766945015860861271926445

However only one is in the interval, yet the other is within the range that i can add another pi to get 1.373400766945015860861271926445 and 4.5149934205348090993239153097245 and  1.7681918866447773776013714568345 and 4.909784540234570616064014840114

So there are 4 possible solutions, not two?

anonymous · Answer

Answer please?

jim_thompson5910 · Answer

I count four solutions as well

jim_thompson5910 · Answer

makes sense because each equation tan(x) = 5, tan(x) = -5 brings 2 solutions each