$Find the values of tan(θ) for specific angles on the unit circle$

$For \ θ = \frac{3π}{4}, \ we \ know \ that \ tan(θ) = \frac{sin(θ)}{cos(θ)}$

$sin(θ) = sin(\frac{3π}{4}) = \frac{1}{\sqrt{2}}, \ cos(θ) = cos(\frac{3π}{4}) = -\frac{1}{\sqrt{2}}$

$Therefore, \ tan(θ) = \frac{\frac{1}{\sqrt{2}}}{-\frac{1}{\sqrt{2}}} = -1$

$For θ = frac{2π}{3}, we know that tan(θ) = frac{sin(θ)}{cos(θ)}$

$sin(θ) = sin(frac{2π}{3}) = frac{sqrt{3}}{2}, cos(θ) = cos(frac{2π}{3}) = -frac{1}{2}$

$Therefore, tan(θ) = frac{frac{sqrt{3}}{2}}{-frac{1}{2}} = -sqrt{3}$

$For θ = frac{5π}{6}, we know that tan(θ) = frac{sin(θ)}{cos(θ)}$

$sin(θ) = sin(frac{5π}{6}) = frac{1}{2}, cos(θ) = cos(frac{5π}{6}) = -frac{sqrt{3}}{2}$

$Therefore, tan(θ) = frac{frac{1}{2}}{-frac{sqrt{3}}{2}} = -frac{1}{sqrt{3}}$

Start Using PopAi Today