Question

Sabendo que cotgx = -2,4 e que 3pi/2<x<2pi, calcule a soma de senx+cosx

Answer 1

cotg=cosx/senx

-2,4=cosx/senx

-2,4senx=cosx

sen²x+cos²x=1

sen²+(-2,4senx)²=1

sen²x+5,76sen²x=1

6,76sen²x=1

sen²x=25/169

senx=+/-5/13

4° quadrante

senx=-5/13

sen²x+cos²x=1

(-5/13)²+cos²x=1

25/169+cos²x=1

cos²x=169/169-25/169

cos²x=144/169

cosx=+/-12/13

4°quadrante

cosx=12/13

senx+cosx

5/13+12/13

17/13