Question

Solve along the interval [theta between 0 and 2pi]"
sin(3theta)=-1

Answer 1

do you mean \[\sin(3 \theta)=-1\]?

Answer 2

A little more eloquently put:\[\sin (3\theta)=-1\]

Answer 3

OK.
Let's draw


What do you think the correct angle matches this equation?

Answer 4

The bottom, where the ordered pair is (0,-1).

Answer 5

Great!

Answer 6

so we can say that:
\[3\theta=\frac{ -\pi }{ 2 } +n.2\pi\]
if theta in radian.

Answer 7

and \[3\theta=-90+n*360\]
if it is in degree.

Answer 8

Do you follow?

Answer 9

Explain how you get "+n.2pi" above, and where n came from.

Answer 10

Firstly, your theta in radian or degree?

Answer 11

Radians.

Answer 12

Ok
Origanally, your answer would be
\[3\theta=\frac{ -\pi }{ 2 }\]
\[\theta=\frac{ -\pi }{ 6 }\]

and we know that every angle theta is equal to its sisters with the addition of 2pi and 4pi and 6pi .....
e.g:
if a=30
then a=30+2pi=30+4pi=30+6pi=30+n(2pi) where n is 0,1,2,3,.....

Answer 13

Ok, that makes sense

Answer 14

Did you get it?

Answer 15

I understand all you said there, but you made no mention of how you incorporated the "n' in it.

Answer 16

Yes, I did.
"if a=30
then a=30+2pi=30+4pi=30+6pi=30+n(2pi) where n is 0,1,2,3,....."

Answer 17

I understand

Answer 18

So can you share me the final result you are comfortable with?

Answer 19

Is the the same as saying\[\sin \theta=-1/3\] ?

Answer 20

Not quite right.
\[\sin(3\theta)=-1\]
\[\sin^{-1}(-1)=3\theta\]
\[3\theta=\frac{ -\pi }{ 2 }\]
\[\theta=\frac{ -\pi }{ 6 }\]

and if you want:
\[\theta=\frac{ -\pi }{ 6 }+n.\frac{ 2\pi }{ 3 }\]
but don't care of that if it would confuse you!

Answer 21

Got it

Answer 22

Thank God!

Answer 23

Thank you for the medal!

Answer 24

My feeling as well. Enough math for one day.

Answer 25

notice they want only the solutions
the interval [theta between 0 and 2pi]"
your solution is for all values of theta, so you have to pick out only the few between 0 and 2pi