How do you find the exact value of $tan (\frac{3 π}{4})$ $tan ( (3pi)/4)$ ?

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Answer 1 · 2016-07-09T06:56:00

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

$tan (\frac{3 π}{4}) = \frac{sin (\frac{3 π}{4})}{cos (\frac{3 π}{4})}$ $tan((3pi)/(4))=sin((3pi)/(4)) / cos((3pi)/(4))$

Knowing the unit circle, we can see that

$sin (\frac{3 π}{4}) = \frac{\sqrt{2}}{2}$ $sin((3pi)/(4)) = (sqrt(2))/(2)$

and

$cos (\frac{3 π}{4}) = - \frac{\sqrt{2}}{2}$ $cos((3pi)/(4)) = -(sqrt(2))/(2)$

so

$tan((3pi)/(4))=(((sqrt(2))/(2)) * (-2/sqrt(2))) / cancel(((-(sqrt(2))/(2))* (-2/sqrt(2))))$

$tan((3pi)/(4))=(-2*cancel(sqrt(2)))/(2*cancel(sqrt(2))) =-2/2=-1$

How do you find the exact value of tan ( (3pi)/4)tan(3π4) tan ( (3pi)/4)?