Test: Trigonometric Equations I - Challenging

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Question 1:   Solve the equation cos π 8 4x =1 .
x=  π 8 πn 2 , nΖ
x=  π 32 πn 2 ,nΖ
x=  π 8 2πn, nΖ
x=  π 32 2πn,nΖ
Question 2:   Find the biggest negative root of the equation sin 3x π 15 =1 .
x= 13π 90
x= 17π 90
x=π
x= 13π 45
Question 3:   Find the sum of the roots of the equation tg2x= 3 , which belong to the range π; π 2 .
π 2
π 3
π 6
5π 6
Question 4:   Solve the equation arccosx= 1 3 .
π 3
sin 1 3
   1 3
 cos 1 3
Question 5:   Solve the inequality arctg 4x5 > π 3 .
x 5; π 3
x 5 3 4 ;+
x π 3 ;5
x ; 5 3 4
Question 6:   Solve the equation 2sinxcosx+ cos 2 x=1 .
x=πn x=arctg2+πn  nΖ
x=πn, nΖ
x=arctg2
x= π 2 +πn, nΖ
Question 7:   Solve the equation cosx+tgx=0 .
x= 1± 5 2
x= 1 n arcsin 1 5 2 +πn, nΖ
x= 1 n arcsin 1± 5 2 +πn, nΖ
x=arcsin 1 5 2 +2πn, nΖ
Question 8:   Solve the equation cos2x  cosx=0 .
x= π 4 + πn 2 ; π 2 +πn,  n ϵ Ζ; 
x= π 2 +πn, n ϵ Ζ
1 2 ;1
x= π 4 + πn 2 , n ϵ Ζ
Question 9:   Solve the inequality sinx< 3 2 .
x π 3 +2πn; 7π 3 +2πn , nΖ
x< π 3
x π 3 +2πn; 2π 3 +2πn , nΖ
x 2π 3 +2πn; 7π 3 +2πn , nΖ
Question 10:   Solve the equation sin3x+sinx=sin2x .
x= πn 2 ,± π 3 +2πn,  n ϵ Ζ 
x= πn 2 , n ϵ Ζ 
x=2πn, n ϵ Ζ 
x=± π 3 +2πn,  n ϵ Ζ