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

**kl050196** · January 16th 2012, 01:56 AM

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 ==

**princeps** · January 16th 2012, 02:46 AM

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 ==

$\sec \theta = \frac {1}{\cos \theta } \Rightarrow \cos \theta = \frac {1}{\sec \theta} \Rightarrow \cos \theta = \frac{1}{2} \Rightarrow$

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

**kl050196** · January 16th 2012, 05:53 AM

what's the 2kpi at the end?

**princeps** · January 16th 2012, 06:27 AM

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...

**HallsofIvy** · January 16th 2012, 06:44 AM

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 $\theta$ . Use the Pythagorean theorem to find the length of the "opposite side". $tan(\theta)$ is, of course, "opposite side over near side".

**kl050196** · January 16th 2012, 04:04 PM

OOOOOOO now i see, thanks sooo much princeps and HallsofIvy

**kl050196** · January 16th 2012, 04:04 PM

Thank youuuu

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

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