Question

решить тригонометрические уравнения! 1) cosx+1/2=0
2) 2sinx=√3
3) sin3x=-1
4) tgx+2=0
5) (ctgx+1)(tgx-1)=0

Answer 1

1)

x1 =2$\pi$/3+2k$\pi$

x2 =4$\pi$/3+2k$\pi$

2)

x1 =$\pi$/3+2k$\pi$

x2 =2$\pi$/3+2k$\pi$

3)

x1 =$\pi$/2+2k$\pi$/3

4)

x = -arcos(2) + k$\pi$

5)

x = $\pi$/4+k$\pi$/2

Объяснение:

1) cos(x)+1/2 =0

cos(x) = -1/2

x1 =2$\pi$/3+2k$\pi$

x2 =4$\pi$/3+2k$\pi$

2) 2sin(x)=$\sqrt{3\\}$

sin(x) =$\sqrt{3}$/2

x1 =$\pi$/3+2k$\pi$

x2 =2$\pi$/3+2k$\pi$

3) sin3x=-1

x1 =$\pi$/2+2k$\pi$/3

4)  tgx+2=0

tgx = -2

x $\neq$$\pi$/2+k$\pi$

x = -arcos(2) + k$\pi$

5) (ctgx+1)(tgx-1)=0

(ctgx+1)(tgx-1) = -2/tan(2x)

x = $\pi$/4+k$\pi$/2