Question

sabiendo que cotg x=1/2, halla las demás funciones trigonométricas

Answer 1

Usamos las relaciones trigonométricas apropiadas

                             tag x = 2                             tag x = (sen x) / (cos x) = 2
                                         sen x = 2cos x

                             sen^2 x + cos^2 x = 1
                             (2 cos x)^2 + cos^2 x = 1 

                             4cos^2 x + cos^2x = 1                              
                             5cos^2 x = 1
                              cos^2 x = 1/5
                               cos x = √(1/5) = 1/√5 = +/- (√5)/5
Tomando valor positivo (necesario saber en que cuadrante está x)

                              cos x = (√5)/5
                               sen x = 2(√5)/5 = (2√5)/5

                               tag x = 2
                               ctg x = 1/2
                               sec x = 1/(cos x) = 1/[(√5)/5] = √5
                               csc x = 1/(sen x) = 1/[2(√5)/5] = (√5)/2