Question

4 sin theta + 3 root 3 = root 3

Answer 1

You are given\[4 \sin(\theta) + 3\sqrt{3} = \sqrt{3}\] and need to solve for \(\theta\) correct?

Answer 2

yes

Answer 3

First, subtract \(3\sqrt{3}\) from both sides.

Answer 4

did that

Answer 5

@MRVerdi, show what you got afterwards.

Answer 6

4 sin theta = 3?

Answer 7

Let me ask you something. Does x - 3x = 3?

Answer 8

no x=-3/2

Answer 9

You are very confused

Answer 10

....

Answer 11

What is 1 - 3 ?

Answer 12

-2

Answer 13

Okay so...

x - 3x = (1 - 3)x = -2x

Answer 14

if you solving for x then you have to divide by -2

Answer 15

Similarly
\(\sqrt{3} - 3\sqrt{3} = (1 - 3)\sqrt{3} = -2\sqrt{3}\)

Answer 16

There is something about this that you are confused about. You're not solving for x. You are simply subtracting.

Answer 17

sorry i misunderstood what you were asking

Answer 18

then how do you divide the -2 root 3 by 4?

Answer 19

You should end up with

\[\sin(\theta) = -\frac{2\sqrt{3}}{4}\]

Now take the inverse sine of both sides to isolate \(\theta\)

Answer 20

\[4 \sin \theta + 3 \sqrt 3 = \sqrt 3 \implies 4 \sin \theta = -2 \sqrt 3 \implies \sin \theta =- \frac{\sqrt3}{2}\]\[\implies \theta= - \frac {\pi}{3} + 2k \pi ~~or~~ \theta = - \frac {2\pi}{3} + 2k \pi\]

Answer 21

Depending on your text, the first term of the two answers might have to be positive as a matter of convention. That would mean the answers would look like \[\theta = \frac{4 \pi}{3} + 2k \pi ~~or~~ \theta = \frac{5 \pi}{3} + 2k \pi\] The main thing about this problem is to work it to a familiar form. Then you HAVE to recognize the special values of the functions, and know where on the unit circle they occur.

Answer 22

@AnimalAin, if you noticed, I was trying to help the user solve it step by step.

Answer 23

The plus 2k pi takes into account that every time you come past that point on the unit circle, you will get a correct answer. Note that k is any integer.

Answer 24

Sorry if I interrupted.