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sec 11pi/3

Use the fact that there are 2pi radians in each circle to find another angle, smaller than 2pi, that is equivalent to 11pi/3.

Respuesta :

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

[tex]\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) [/tex]

[tex]= \sec\left(-\dfrac{\pi}{3}\right) = \dfrac{1}{\cos(-\frac{\pi}{3})} = \dfrac{1}{\cos \frac \pi 3}= \dfrac{1}{\frac 1 2} = 2[/tex]

lublana

Answer:

[tex]sec\frac{11\pi }{3} =2[/tex]

Step-by-step explanation:

Given

[tex]sec\frac{11\pi }{3}[/tex]

= [tex]sec( 4\pi -\frac{\pi }{3})[/tex]

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

[tex]sec\frac{11\pi }{3} =sec\frac{\pi }{3}[/tex]

Because [tex]sec(2\pi -\theta)= sec\theta[/tex]

Because [tex]sec\theta[/tex] is positive in first quadrant and IV quadrant . There is [tex]\theta[/tex] lies in the IV quadrant .

Hence, [tex]sec\frac{\pi }{3}[/tex] is positive in IV quadrant .

[tex]sec\frac{11\pi }{3} =sec\frac{\pi }{3}[/tex]

We know that value of [tex]sec\frac{\pi }{3} =sec60^{\circ}=2[/tex]

Therefore, [tex]sec\frac{11\pi }{3} =2[/tex].

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