Question

Need help??
I have the problem
-3tan^2(2x)+1=0
And I am having trouble solving it.. This is where I've gotten so far.
-3tan^2 (2x)=1
-3tan^2(x)=1/2
This is where I get stuck lol can anyone help?

Answer 1

@robtobey

Answer 2

First off, you should have -1 on right side after step 1

Second, the "2" in tan(2x) is attached to the tan function and cannot be divided on both sides

Answer 3

@dumbcow You're right..
\[-3\tan^{2}2x=-1\]

Answer 4

Then what?

Answer 5

Originally think of the equation as
\[-3u^2 +1 = 0\]
where i replaced tan function with variable u
it can be easier to solve if you are not confused by the trig

Answer 6

So
-3u^2=-1
Would you then factor -3u^2?

Answer 7

how would you factor that? remember its only 1 term

Answer 8

u^2= -1/-3
u^2=1/2
sqrt(^2)=sqrt(1/2)?

Answer 9

Tht should be a 3,, not 2.

Answer 10

very good

Answer 11

My bad.
Okay, so would it plus and minus?

Answer 12

Not lets put back in the tan
.... yes plus minus
\[u = \pm \frac{\sqrt{3}}{3}\]
\[\tan(2x) = \frac{\sqrt{3}}{3}\]
You must use inverse tangent to cancel the tan function to get to the "x"
\[2x = \tan^{-1} (\frac{\sqrt{3}}{3})\]

Answer 13

use calculator or unit circle to find angles

sorry i for got plus minus ... you also look up inverse tan of neg sqrt3/3

Answer 14

have you found the angles?

Answer 15

ok this is what you should get from your calculator (using degrees)
\[\tan^{-1} \pm \frac{\sqrt{3}}{3} = \pm 30\]
Note the period for tangent is 180 so if you need all solutions, add multiples of 180

\[2x = \pm 30 + 180n\]
Finally solve for x by dividing by 2
\[x = \pm 15 +90n\]

Answer 16

Thanks @dumbcow ! I actually got x= +/- 15 but forgot the 90n. Thank you! I don't feel so dumb now thanks to you.

Answer 17

I had forgot bout the period of the tangent being 180

Answer 18

haha no problem , glad to help