Question

Tan^2x + Tanx = 0
find all real solutions

Answer 1

What's your best attempt? Doesn't this look a lot like solving a quadratic formula except we have tanx instead of x?

Answer 2

i factored out a tanx and got tanx ( tanx +1) = 0
so tanx = -1 ?

Answer 3

which may be -45

Answer 4

??

Answer 5

Yeah you're right! You have two equations though, and that's only one part of one answer. Remember that trig functions are also periodic.

Answer 6

yes i got 3pi/4 and 7pi/4 because the negative 45

Answer 7

When you factor out tangent you get:

tanx(tanx+1)=0

So you need to solve:

tanx=0
AND
tanx=-1

and both of these have periodic solutions, so you will have an infinite number of solutions every 2pi at least.

Answer 8

ooh yes i forgot the tanx=0

Answer 9

Although each one is actually going to have more than one solution every 2pi. For instance, for tanx=0 the answer isn't just x=0 but also x=pi between 0 and 2pi.

But these repeat infinitely so if you just say n is any integer, then
\[x=n \pi\] is the answer since you can plug in n=2 or n=4 or n=-1 or whatever and you will get the right answer since it's cyclic. But you need to find the same answers for tanx=-1 since this is only half the answer.

Answer 10

yes that is helpful. i didnt tell you the interval is from 0 to 2pi

Answer 11

Oh I thought you said find all real solutions lol. Ok well then you know what to do .

Answer 12

thank you, those were the limits