Question

Sec 11pi/3

Answer 1

Answer:

$sec\frac{11\pi }{3} =2$

Step-by-step explanation:

Given

$sec\frac{11\pi }{3}$

= $sec( 4\pi -\frac{\pi }{3})$

It lies in the IV quadrant .Therefore we can write as

$sec\frac{11\pi }{3} =sec\frac{\pi }{3}$

Because $sec(2\pi -\theta)= sec\theta$

Because $sec\theta$ is positive in first quadrant and IV quadrant . There is $\theta$ lies in the IV quadrant .

Hence, $sec\frac{\pi }{3}$ is positive in IV quadrant .

$sec\frac{11\pi }{3} =sec\frac{\pi }{3}$

We know that value of $sec\frac{\pi }{3} =sec60^{\circ}=2$

Therefore, $sec\frac{11\pi }{3} =2$.

Answer 2

I prefer the word "coterminal" to equivalent; coterminal angles have all the same values for their trig functions.  They differ by $2\pi k, \quad$ integer $k$.

$\sec \dfrac{11 \pi}{3} = \sec\left( \dfrac{ 11 \pi}{3} - 4\pi \right) = \sec\left( \dfrac{ 11 \pi}{3} - 4\pi \right) = \sec\left( \dfrac{ 11 \pi}{3} - \dfrac{12\pi}{3} \right)$

$= \sec\left(-\dfrac{\pi}{3}\right) = \dfrac{1}{\cos(-\frac{\pi}{3})} = \dfrac{1}{\cos \frac \pi 3}= \dfrac{1}{\frac 1 2} = 2$