Question

Sa se calculeze ctgx, stiind ca sinx = $\frac{\sqrt{3} }{2}$ x apartine (0,90)

Answer 1

Din formula fundamentala a trigonometriei:

$\cos{x} = \sqrt{1 - sin^2 x} = \sqrt{1 - \frac{3}{4}} = \sqrt{\frac{1}{4}} = \frac{\sqrt{1}}{\sqrt{4}} = \frac{1}{2}$

$ctg x = \frac{\cos{x}}{\sin{x}} = \frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}} = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}$