Test: Trigonometric Equations I - Ambitious

Double click on maths expressions to zoom
Question 1:   Solve the equation cos4x= 2 2 .
 ± 3π 16 + πn 2 ,nΖ
 ± 3π 16 +2πn,nΖ
 ± 3π 4 +2πn,nΖ
 ± 1 n+1 ×π 16 + πn 4 ,nΖ
Question 2:   Solve the equation sin t+ π 8 =1 .
5π 16 +2πn,nΖ
1 n+1 ×5π 8 +πn,nΖ
5π 8 +2πn,nΖ
5π 8 +πn,nΖ
Question 3:   Solve the equation ctgx= 3 3   .
x= π 3 +2πn,nΖ
x= π 3 +πn,nΖ
x= π 6 +πn,nΖ
x= π 3 +πn,nΖ
Question 4:   Solve arcsin 3 5 +arccos 3 5 .
1
0
2π
π 2
Question 5:   Solve the equation arcctg 58x = 2π 3 .
152π 24
15+ 3 24
5+ 3 8
1 2
Question 6:   Solve the inequality 1cos2x sin 2 x>0 .
x 0;1
x 2πn; 2πn+π , n Ζ
x πn; πn+π , n Ζ 
x 0; 2πn , n Ζ  
Question 7:   Solve the equation sin3x+sinx=sin2x .
x= πn 2 ,n Ζ 
πn 2 , ± π 3 +2πn,n Ζ    
± π 3 +2πn,n Ζ   
   
Question 8:   Solve the inequality ctgx 3 .
x πn; 5π 6 +πn , nΖ
x πn; 5π 6 +πn , nΖ
x πn; 5π 6 +πn , nΖ
x 0; 5π 6
Question 9:   Solve this system of equations x+y= π 3 sinx=1 .
π 2 +2πn;  π 6 2πn , nΖ
π 2 2πn;  π 6 2πn , nΖ
π 2 +2πn;  π 6 +2πn , nΖ
π 2 +2πn;  π 6 2πn , nΖ 
Question 10:   Solve the equation tgx+ 1 cos 2 x =3 .
π 4 +πn; arctg2+πn,nΖ
π 4 +2πn; arctg2+2πn,nΖ
π 4 ; arctg2 
π 4 +πn,nΖ