Question

Rozwiąż równanie a)sinx=|x|/x

b)cos x-|x|/2=1

Answer 1

a)

sinx = IxI/x

D. x =/= 0

x > 0 ---> sinx = x/x =1

x =pi/2 + 2kpi

k e {0,1,2,3,.....}

 

x < 0 ---> sinx = -x/x =-1

x = -pi/2 - 2kpi

k e {0,1,2,3,......]

b)

cos(x- IxI/2) =1

x >= 0 ---> (x-x)/2 = 0

cos 0 =1

 

x < 0 ---> (x+x)/2 = x

cosx =1

x = -2kpi

k e N

 

x e {......, -4pi, -2pi} U < 0, +oo)