How do you find the exact value of all 6 trigonometric functions for the angle 11*pi / 6?

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How do you find the exact value of all 6 trigonometric functions for the angle 11*pi / 6?

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Answer 1 · 2015-10-19T06:26:22

$cos θ = \frac{\sqrt{3}}{2}$ $cos theta = sqrt(3)/2$
$sec θ = \frac{2}{\sqrt{3}}$ $sec theta = 2/sqrt(3)$
$sin θ = - \frac{1}{2}$ $sin theta = -1/2$
$cos e c θ = - 2$ $cosec theta = -2$
$tan θ = - \frac{1}{\sqrt{3}}$ $tan theta = -1/sqrt(3)$
$cot θ = - \sqrt{3}$ $cot theta = -sqrt(3)$

Explanation:

$11 \frac{π}{6} = 2 π - \frac{π}{6}$ $11pi/6 = 2pi - pi/6$
lies in the 4th quadrant
cos and sec are positive and remaining are negative
$cos 2 π - θ = cos θ$ $cos 2pi - theta = cos theta$
so $cos (2 π - \frac{π}{6}) = cos (\frac{π}{6})$ $cos (2pi - pi/6) = cos (pi/6)$
$cos θ = \frac{\sqrt{3}}{2}$ $cos theta = sqrt(3)/2$
so $sec θ = \frac{2}{\sqrt{3}}$ $sec theta = 2/sqrt(3)$
$sin θ = - \frac{1}{2}$ $sin theta = -1/2$
$cos e c θ = - 2$ $cosec theta = -2$
$tan θ = - \frac{1}{\sqrt{3}}$ $tan theta = -1/sqrt(3)$
$cot θ = - \sqrt{3}$ $cot theta = -sqrt(3)$

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How do you find the exact value of all 6 trigonometric functions for the angle 11*pi / 6?

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