Question

cosx=3/5
xE[0, pi/2]
ctgx=?

Answer 1

$\cos \text{x} = \dfrac{3}{5},\quad \text{x}\in \Big[0,\dfrac{\pi}{2}\Big]\\ \\ \sin^2 \text{x} = 1-\cos^2 \text{x} \Rightarrow \\ \\ \Rightarrow \sin^2 \text{x} = 1-\Big(\dfrac{3}{5}\Big)^2 \Rightarrow \\ \\ \Rightarrow \sin^2 \text{x} = 1 - \dfrac{9}{25} \Rightarrow \\ \\ \Rightarrow \sin^2 \text{x}= \dfrac{16}{25} \Rightarrow \sin \text{x} = \pm\dfrac{4}{5}, dar, \text{x}\in \Big[0,\dfrac{\pi}{2}\Big] \Rightarrow$
$\Rightarrow \sin \text{x} = \dfrac{4}{5} \\ \text{ctg x} = \dfrac{\cos \text{x}}{\sin \text{x}} =\dfrac{\dfrac{3}{5}}{\dfrac{4}{5}} = \dfrac{3}{4} \\ \Rightarrow \boxed{\text{ctg x} = \dfrac{3}{4}}$