Question

Pre calc question~ Help please!

So, for the question below, I'm supposed to mark any solutions for the equation: tan^2x-3=0.

My options are:

A. 2pi/3
B. pi
C. -pi/3
D. 5pi/3

I keep coming up with A and C as the answer, however those choices aren't correct.

Answer 1

@ganeshie8 help please? :)

Answer 2

like this?
\[\tan^{2x-3}=0\]

Answer 3

@nincompoop Here's what it looks like on my assignment!

Answer 4

One way to do it is to check each one using this approach:

tan^2(2pi/3)-3=0
tan^2(pi)=0
tan^2(-pi/3)-3=0
tan^2(5pi/3)-3=0

Answer 5

The other way to do it is to actually solve for x:

\(\tan(x)^2 - 3 = 0\)
\(\tan(x)^2 = 3\)
\(\tan(x) = \pm\sqrt{3}\)
\(x = \tan^{-1}(\pm \sqrt{3})\)

Answer 6

For the first approach, I'd just plug the solutions into the equation? and if they come out whole, they'd be an answer?

Answer 7

For the first approach, a given expression must equal zero to be correct.

Answer 8

Be sure to put your calc in radian mode

Answer 9

Got it! That makes sense now. Thank you :)

Answer 10

Wait, so now all I have for solutions is pi?

Answer 11

I was going to mention that if you solved it the other way you must add the period of tan to your original solutions to get other values

Answer 12

Oh. Sorry, I'm very bad at math in this form, how would I add the period of tan into the whole thing?

Answer 13

Ah, okay. When I only used pi as an answer, it said I needed one more... Which is why I'm so confused! Thank you for your help though, at least I know how to approach similar problems now.

Answer 14

What's interesting is you mentioned that you originally got A and C as the correct choices. That's the same thing I get when I check.

Answer 15

But I also get one more as well

Answer 16

Oh! Did you get D as the third one?

Answer 17

Yes and desmos.com confirms:

https://www.desmos.com/calculator/a898xwnb3s

Answer 18

Thank you so much!

Answer 19

Just to emphasize, I plotted some points on the graph here:
https://www.desmos.com/calculator/5uq6uammlf

Answer 20

The visual does help me understand it more.

Answer 21

:)