Question #9ed58

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Question #9ed58

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Answer 1 · 2016-12-21T02:51:16

$sec (\frac{5 π}{6}) tan (- \frac{π}{6}) = \frac{2}{3}$ $sec((5pi)/6)tan(-pi/6)=2/3$

Explanation:

Assuming 'x' is referring to multiplication, we will use the following:

Definitions of $sec$ $sec$ and $tan$ $tan$ :

$sec (θ) = \frac{1}{cos (θ)}$ $sec(theta) = 1/cos(theta)$
$tan (θ) = \frac{sin (θ)}{cos (θ)}$ $tan(theta) = sin(theta)/cos(theta)$

$sin$ $sin$ is odd and $cos$ $cos$ is even:

$sin (- θ) = - sin (θ)$ $sin(-theta) = -sin(theta)$
$cos (- θ) = cos (θ)$ $cos(-theta) = cos(theta)$

Well known angles:

$sin (\frac{π}{6}) = \frac{1}{2}$ $sin(pi/6) = 1/2$
$cos (\frac{π}{6}) = \frac{\sqrt{3}}{2}$ $cos(pi/6) = sqrt(3)/2$
$cos (\frac{5 π}{6}) = - \frac{\sqrt{3}}{2}$ $cos((5pi)/6) = -sqrt(3)/2$

With those, we have

$sec (\frac{5 π}{6}) tan (- \frac{π}{6}) = \frac{1}{cos (\frac{5 π}{6})} ⎛ ⎜ ⎝ \frac{sin (- \frac{π}{6})}{cos (- \frac{π}{6})} ⎞ ⎟ ⎠$ $sec((5pi)/6)tan(-pi/6) = 1/cos((5pi)/6)(sin(-pi/6)/cos(-pi/6))$

$= \frac{1}{cos (\frac{5 π}{6})} ⎛ ⎜ ⎝ \frac{- sin (\frac{π}{6})}{cos (\frac{π}{6})} ⎞ ⎟ ⎠$ $=1/cos((5pi)/6)((-sin(pi/6))/cos(pi/6))$

$= \frac{1}{- \frac{\sqrt{3}}{2}} ⎛ ⎜ ⎝ \frac{- \frac{1}{2}}{\frac{\sqrt{3}}{2}} ⎞ ⎟ ⎠$ $=1/(-sqrt(3)/2)((-1/2)/(sqrt(3)/2))$

$= \frac{2}{3}$ $=2/3$

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Question #9ed58

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