Question

Se da Cos alfa = 1/5 , alfa € c
Se cere : sin alfa,tg alfa,ctg alfa
Ajutorrrr !!!!

Answer 1

 

$\displaystyle\bf\\\textbf{cos este pozitiv in cadranul 4.}\\\\\textbf{Celelalte (sin, tg, ctg) sunt negative in cadranul 4.}\\\\Rezolvare:\\\\cos\propto=\frac{1}{5} \\\\sin\propto=-\sqrt{1-cos^2\propto}=-\sqrt{1-\Big(\frac{1}{5}\Big)^2}=\\\\=-\sqrt{1-\frac{1}{25}}=-\sqrt{\frac{24}{25}}=-\frac{\sqrt{4\times6}}{\sqrt{25}}= \boxed{\bf -\frac{2\sqrt{6}}{5}}$

.

$\displaystyle\bf\\tg\propto=\frac{sin\propto}{cos\propto}=\frac{-\dfrac{2\sqrt{6}}{5}}{\dfrac{1}{5}}=-\dfrac{2\sqrt{6}}{5}\times\frac{5}{1}=\boxed{\bf-2\sqrt{6}}\\\\\\ctg\propto=\frac{1}{tg\propto}=\frac{1}{-2\sqrt{6}}=-\frac{\sqrt{6}}{2\sqrt{6}\times\sqrt{6}}=-\frac{\sqrt{6}}{2\times6}=\boxed{\bf-\frac{\sqrt{6}}{12}}$