General Solutions

[carebear]

I have been asked to solve cos 2theta = 1/2 and theta is an element of the Real Number System.

The answer that I arrived at is
pi/6 + 2kpi, k is an integer,
5pi/6 + 2kpi, k is an integer,
7pi/6 +2kpi, k is an integer, and
11pi/6 + 2kpi, k is an integer

Is that correct? and could I write it as theta = {pi/6, 5pi/6, 7pi/6, 11pi/6} + 2kpi, k is an integer?

 

[Deleted member 4993]

I have been asked to solve cos 2theta = 1/2 and theta is an element of the Real Number System.

The answer that I arrived at is
pi/6 + 2kpi, k is an integer,
5pi/6 + 2kpi, k is an integer,
7pi/6 +2kpi, k is an integer, and
11pi/6 + 2kpi, k is an integer

Is that correct? and could I write it as theta = {pi/6, 5pi/6, 7pi/6, 11pi/6} + 2kpi, k is an integer?

I would write it as follows:

\(\displaystyle \theta \ = \ \pm \frac{\pi}{6} \ \pm \ k*\pi\)

where k is an integer

 

[carebear]

Thank you.....I understand the +/- pi/6 would I need the +/- in front of k when k is an integer anyways?

 

[Deleted member 4993]

Thank you.....I understand the +/- pi/6 would I need the +/- in front of k when k is an integer anyways?

You are correct - the ± in front of 'k' is not necessary, however it is not wrong.