Question

20 POINTS. Given cos θ=4/5, find cot(θ).

Answer 1

 

$\displaystyle\\\cos\theta=\frac{4}{5}\\\\ \sin\theta=\sqrt{1-\cos^2\theta}=\sqrt{1-\left(\frac{4}{5}\right)^2} =\sqrt{1-\frac{16}{25}} =\sqrt{\frac{9}{25}} =\frac{3}{5}~~\text{(If } \theta \in \text{quadrant 1)}}\\\\\\ \cot(\theta)=\frac{\cos\theta}{\sin\theta}=\frac{~~\dfrac{4}{5}~~}{\dfrac{3}{5}}=\frac{4}{5}\times\frac{5}{3}=\frac{4}{3}\\\\\\\boxed{\cot(\theta)=\frac{4}{3}}$

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