Given ${csc θ}^{\circ} = \frac{\sqrt{3}}{2}$ $csctheta^circ=sqrt3/2$ and ${sec θ}^{\circ} = \frac{\sqrt{3}}{3}$ $sectheta^circ=sqrt3/3$ , how do you find $tan θ$ $tantheta$ ?

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Answer 1 · 2017-01-10T06:46:33

The answer is $= \frac{2}{3}$ $=2/3$

By definition,

$csc θ = \frac{1}{sin θ}$ $csctheta=1/sintheta$

$sec θ = \frac{1}{cos θ}$ $sectheta=1/costheta$

$tan θ = \frac{sin θ}{cos θ}$ $tantheta=sintheta/costheta$

$= \frac{sec θ}{csc θ}$ $=sectheta/csctheta$

$= \frac{\frac{\sqrt{3}}{3}}{\frac{\sqrt{3}}{2}}$ $=(sqrt3/3)/(sqrt3/2)$

$=cancel(sqrt3)/3*2/cancel(sqrt3)$

$=2/3$

Given csctheta^circ=sqrt3/2cscθ∘=√32csctheta^circ=sqrt3/2 and sectheta^circ=sqrt3/3secθ∘=√33sectheta^circ=sqrt3/3, how do you find tanthetatanθtantheta?