Question

Find all the solutions of tan)x_^2-tan(x)-6=0 on the interval 0,2pi
possible answers x = arctan(3), x = pi - arctan(3), x = pi + arctan(2), x = pi - arctan(2)
x = arctan(3), x = pi + arctan(3), x = 2pi -arctan(2), x = pi - arctan(2)
x = arctan(3), x = pi + arctan(3), x = -arctan(2),x = -pi - arctan(2)
The equation has no solutions on the interval [0, 2pi).

I believe it is b because its the only one that fits the parameters.

Answer 1

Is it \[(\tan(x))^2 - \tan(x) - 6 = 0\] ?

Answer 2

yes thats what i meant

Answer 3

\[(\tan(x))^2 - \tan(x) - 6 = (\tan(x)-3) * (\tan(x)+2) = 0 \\
\tan(x) = 3 \text{ or } \tan(x) = -2\]

Answer 4

So b, since the others arent in the interval?

Answer 5

Not clear which one is b.

Answer 6

x = arctan(3), x = pi + arctan(3), x = 2pi -arctan(2), x = pi - arctan(2)

Answer 7

Yes.

Answer 8

thanks

Answer 9

yw.