How do you find the values of the six trigonometric functions given $tan θ$ $tantheta$ is undefined and $π \leq θ \leq 2 π$ $pi<=theta<=2pi$ ?

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Answer 1 · 2017-05-22T22:52:44

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$tan θ = undefined$ $tantheta="undefined"$ and $π \leq θ \leq 2 π$ $pi <= theta <= 2pi$

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

Since $tan θ$ $tantheta$ is undefined, $cos θ = 0$ $costheta=0$ . Therefore $θ = \frac{3}{2} π$ $theta=3/2pi$ .

$sin (θ) = sin (\frac{3}{2} π) = - 1$ $sin(theta)=sin(3/2pi)=-1$

$csc (θ) = \frac{1}{sin θ} = - 1$ $csc(theta)=1/sintheta=-1$

$sec (θ) = \frac{1}{cos θ} = undefined$ $sec(theta)=1/costheta="undefined"$

$cot (θ) = \frac{cos θ}{sin θ} = 0$ $cot(theta)=costheta/sintheta=0$

How do you find the values of the six trigonometric functions given tanθtantheta is undefined and π≤θ≤2πpi<=theta<=2pi?