Question

Помогите с математикой, пожалуйста!

Answer 1

1) sin(5x/3)=0

5x/3=πn; n∈Z

x=3πn/5; n∈Z

2) 2sinт(3x+π/4)-√2=0

2sinт(3x+π/4)=√2

sinт(3x+π/4)=√2/2

3x+π/4=(-1)ⁿπ/4+πn; n∈Z

3x=(-1)ⁿπ/4+πn-π/4; n∈Z

x=(-1)ⁿπ/12+πn/3-π/12; n∈Z

3)cos(x-π/5)=-1/2

x-π/5=±2π/3+2πn; n∈Z

x=π/5±2π/3+2πn; n∈Z

4) 2cos(π/3-4x)-2=0

2cos(π/3-4x)=2

cos(π/3-4x)=1

cos(4x-π/3)=1

4x-π/3=2πn; n∈Z

4x=π/3+2πn; n∈Z

x=π/12+πn/2; n∈Z

5) tg(x/2-π/8)=√3

x/2-π/8=arctg√3+πn; n∈Z

x/2=π/8+π/3+πn; n∈Z

x=π/4+2π/3+2πn; n∈Z

x=11π/12+2πn; n∈Z

6)√3ctg(π/4-x)-1=0

√3ctg(π/4-x)=1

ctg(π/4-x)=1/√3

π/4-x=π/3+πn; n∈Z

х=π/4-π/3-πn; n∈Z