Question

how would you solve the given trigonometric equation exactly on 0< or = theta<2pi

3tan(2theta)-squareroot of 3=0

Answer 1

\[3\tan 2\theta =\sqrt{3}\]

Answer 2

Let's look at a similar problem really quick.
\[\large 3\tan \theta-\sqrt3=0\]We would start by adding sqrt3 to each side,\[\large 3\tan \theta=\sqrt3\]Divide each side by 3,\[\large \tan \theta=\frac{\sqrt3}{3}\]Then we would remember back to our special angles and determine that \(\large \theta=\dfrac{\pi}{6}\).

Answer 3

\[\tan 2\theta =\frac{\sqrt{3}}{3}\]

Answer 4

The problem you're working on will be very very similar, can you see the minor difference?

Answer 5

\[2\theta=30, 210, 390. 570\]

Answer 6

um i checked my book to see if i was doing it right and think i'm supposed to come up with 4 answers... i have 2 but i dont see why i needed the other two..

Answer 7

\[\theta= 15,105, 195, 285\]

Answer 8

\[\theta=\pi/12\] and \[\theta=7\pi/12\]

Answer 9

You need the other two because you need to find all the solutions of theta between 0 and 2 pi which means you need all 2theta values between 0 and 4 pi

Answer 10

Hmm yah that's a little bit tricky. So normally you only have 2 angles that produce the given measure yes?

But our angle is written in terms of \(\large 2\theta\).

So you might want to write it out like this,\[\large 2\theta=\frac{\pi}{6}, \qquad \frac{7\pi}{6}, \qquad \frac{13\pi}{6}, \qquad \frac{19\pi}{6}\]
Listing all the angles between 0 and 4pi.
Dividing by 2 shows us that all four of these angles are between 0 and 2pi.

Answer 11

\[\large \theta=\frac{\pi}{12}, \qquad \frac{7\pi}{12}, \qquad \frac{13\pi}{12}, \qquad \frac{19\pi}{12}\]

Answer 12

Hopefully I calculated those other two correctly XD you should check to make sure heh

Answer 13

ok i see why but wait.. how did you get the last two? i keep getting 5pi/12 and 11pi/6 ...

Answer 14

So to get the first angle, you remembered your special angle on the unit circle.
To get the next angle, we travel pi around the circle \(\large \dfrac{\pi}{6}+\pi=\dfrac{7\pi}{6}\).
To find the next angle, travel another pi around.\[\large \frac{7\pi}{6}+\pi \qquad = \qquad \frac{13\pi}{6}\]

Answer 15

oh!! oh my gosh.. ok that makes more sense.. ^_^

Answer 16

then i would divide by two for all four of them right? >.<

Answer 17

ya c:

Answer 18

whoo! ok oh my gosh thank you!!! im so glad i found this site~ :3

Answer 19

hehe