trigonometric equations

The solution set of the equation $\sin x=-\frac{1}{2}$   

for  $<0,2\pi>$  is:

• 
  $\left\{\frac{7\pi}{6},\frac{11\pi}{6}\right\}$
  

• $\left\{\frac{7\pi}{6}\right\}$

• $\left\{\frac{11\pi}{6}\right\}$

• $\left\{\frac{5\pi}{6},\frac{7\pi}{6}\right\}$

How many solutions does the following equation have? $\cos^2x+3\cos x=\sin^2x-2$  for $<-180,540>$  

• 4

• 5

• 6

• 7

The following equation has for  $<0;90>$   solutions $x_1$ and $x_2$ . Find the sum of $x_1$ and $x_2$ .

 $\sin2x=\cos x$ 

The solution set of the equation $2tgx-2\cot gx+3=0$  is:

•  $\left\{26,6\degree+180k;\ 116,6\degree+180k\right\}$  

•  $\left\{63,4\degree+180k;\ 153,4\degree+180k\right\}$  

•  $\left\{26,6\degree+180k\right\}$  

•  $\left\{153,4\degree+180k\right\}$  

The solution set of the equation $\cos\left(2x-\pi\right)=-1$  for  $<0,2\pi>$  is

•  $\left\{0,180,360\right\}$  

•  $\left\{0,360\right\}$  

•  $\left\{0,180\right\}$  

•  $\left\{180,360\right\}$  

The solution set of the equation $\cos\left(\frac{x}{4}\right)=0,4$  is:

•  $\left\{66,4\degree+360k;\ 293,6\degree+360k\right\}$  

•  $\left\{265,6\degree+1440k;\ 1174,4\degree+1440k\right\}$  

•  $\left\{265,6\degree+360k;\ 1174,4\degree+360k\right\}$  

•  $\left\{66,4\degree+1440k;\ 293,6\degree+1440k\right\}$  

The following equation has for  $<0;360>$   solutions $x_1$ and $x_2$ . Find the sum of $x_1$ and $x_2$ .

 $7tgx=15$ 

The solution set of the equation $\sin\left(60+3x\right)=-\frac{\sqrt{2}}{2}$  is:

•  $\left\{225\degree+120k;\ 315\degree+120k\right\}$  

•  $\left\{55\degree+360k;\ 85\degree+360k\right\}$  

•  $\left\{55\degree+120k;\ 85\degree+120k\right\}$  

•  $\left\{165\degree+360k;\ 255\degree+360k\right\}$  

•  $\left\{225\degree+360k;\ 315\degree+360k\right\}$  

The solution set of the equation $\sin^2x+2\sin x-3=0$  for  $<-2\pi,2\pi>$  is

•  $\left\{90\degree\right\}$  

•  $\left\{-270\degree,90\degree\right\}$  

•  $\left\{270\degree\right\}$  

•  $\left\{-270\degree\right\}$  

•  $\left\{-90\degree,\ 270\degree\right\}$  
  

How many solutions does the following equation have? $2\cos^2x+3\cos x=9$ .

•  $\infty$  

• 2

• 0

• 1