# Thread: If sec =2, find the possible values of tan theta

1. ## If sec =2, find the possible values of tan theta

just got a question to ask, If sec =2, find the possible values of tan theta? have to prepare for upcoming test in 2 days ==

2. ## Re: If sec =2, find the possible values of tan theta

Originally Posted by kl050196
just got a question to ask, If sec =2, find the possible values of tan theta? have to prepare for upcoming test in 2 days ==
$\displaystyle \sec \theta = \frac {1}{\cos \theta } \Rightarrow \cos \theta = \frac {1}{\sec \theta} \Rightarrow \cos \theta = \frac{1}{2} \Rightarrow$

$\displaystyle \Rightarrow \theta_1 = \frac{\pi}{3}+2k\pi \land \theta_2= \frac{5\pi}{3}+2k\pi$

3. ## Re: If sec =2, find the possible values of tan theta

what's the 2kpi at the end?

4. ## Re: If sec =2, find the possible values of tan theta

Originally Posted by kl050196
what's the 2kpi at the end?
period of cosine....it is irrelevant for your calculation so you can omit it...

5. ## Re: If sec =2, find the possible values of tan theta

Another way to look at it: draw a right triangle with hypotenuse of length 2 and and "near side" of length 1 so the angle is $\displaystyle \theta$. Use the Pythagorean theorem to find the length of the "opposite side". $\displaystyle tan(\theta)$ is, of course, "opposite side over near side".

6. ## Re: If sec =2, find the possible values of tan theta

OOOOOOO now i see, thanks sooo much princeps and HallsofIvy

Thank youuuu