# Thread: Just need confirmation on a circular function question.

1. ## Just need confirmation on a circular function question.

determine the value of the following if 0 is less than or equal to theta and theta is less than 2 pie.

sec theta= -2root3/3= -root/3= 7pie/6

2. Originally Posted by Dave19
determine the value of the following if 0 is less than or equal to theta and theta is less than 2 pie.

sec theta= -2root3/3= -root/3= 7pie/6
First, it's "pi" not "pie."

Second, what exactly are you asking? These cannot all be equal to one another.

Are you asking to find $\theta$ when
$sec(\theta) = - \frac{2\sqrt{3}}{3}$

$sec(\theta) = -\sqrt{3}$

and to find
$sec \left ( \frac{7 \pi}{6} \right )$

You've been asking for help on a large number of these. Why don't you tell us what you've been able to do so we can help you learn this better.

-Dan

3. ## heres what i have done.

i will put it in steps 1,2,3,4

sec theta= 1)-2root3/3 2) cos theta=1/sec theta 3) after the work it turns to -root3/2 4) then i have it as 7pie/6 and im unsure if there should be 5pie/6 in it to.

4. Originally Posted by Dave19
i will put it in steps 1,2,3,4

sec theta= 1)-2root3/3 2) cos theta=1/sec theta 3) after the work it turns to -root3/2 4) then i have it as 7pie/6 and im unsure if there should be 5pie/6 in it to.
Okay, please in the future don't string those equal signs together like that. It is very confusing!

$sec(\theta) = -\frac{2\sqrt{3}}{3}$

$cos(\theta) = -\frac{\sqrt{3}}{2}$

Now, this implies that we have a reference angle of $\pi / 6$. Cosine is negative in QII and QIII. So your solution will be
$\theta = \pi \pm \frac{\pi}{6}$
so your final solution is both $5\pi / 6$ and $7 \pi / 6$.

-Dan