Question

When are you supposed to use these within trigonometric equations?

Answer 1

For example;
If you end up with the answer
\[\frac{ \pi }{ 4 } and \frac{ \pi }{ 6 } \]

How do you know if its supposed to be
\[\frac{ \pi }{ 4 } + 2k pi\]

\[\frac{ \pi }{ 4 } + k pi \]

Answer 2

I meant to put or between the last 2 equations

Answer 3

Is your question when do you include that in your answer, or which one do you use?

Answer 4

Sorry, but I don't get your question here.

Answer 5

\[\sin(\theta\pm2n\pi)=\sin(\theta)\]
\[\cos(\theta\pm2n\pi)=\cos(\theta)\]
\[\tan(\theta\pm n\pi)=\tan(\theta)\]

Answer 6

Example problem:\[\Large\bf\sf \sin x=\frac{\sqrt2}{2}\]Solving for x gives us,\[\Large\sf \frac{\pi}{4}\text{ and }\frac{3\pi}{4}\]But since we want ALL angles that produce sqrt2/2, we have to allow for full rotations around the unit circle that land us in the same spot.
So your solution would be,\[\Large x=\cases{\frac{\pi}{4}+2k \pi, \\\frac{3\pi}{4}+2k \pi, \qquad k=0,\pm1,\pm2,...}\]
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Alternatively, if you're given the same problem but with a small change,\[\Large\sf \sin x=\frac{\sqrt2}{2},\qquad \qquad 0\le x\lt 2\pi\]This inequality is telling us that we only want the solution in one rotation around the unit circle.
So we would have the same solution but without the +2kpi.