Question

Rozwiąż równania:

a)2cos(-3x)=1
b)2sin(2x-pi)=1

Answer 1

a)

cos3x=1/2

cos(-α)=cosα

 

3x=π/3+2kπ  v 3x=-π/3+2kπ  /:3

x=π/9+2/3kπ v x=-π/9+2/3kπ=5/9π+2/3kπ

 

b) sin(180-α)=sinα    i sin(-α)=-sinα

sin(2x-π)=1/2

 

2x-π=π/6+2kπ v 2x-π=5/6π+2kπ

2x=7/6π+2kπ v 2x=11/6π+2kπ  /:2

x=7/12π+kπ  v x=11/12π+kπ