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How do I find the value of sec 5pi / 6?

1 Answer

Apr 1, 2018

$color(blue)(-(2sqrt(3))/3$

Explanation:

$sec((5pi)/6)$

Identity:

$color(red)bb(sec(x)=1/cos(x))$

$cos((5pi)/6)=-cos(pi-(5pi)/6)=-cos(pi/6)=-sqrt(3)/2$

$sec((5pi)/6)=1/-cos((pi)/6)=1/((-sqrt(3))/2)=color(blue)(-(2sqrt(3))/3$

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