Test: Trigonometric equations I - Normal

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Question 1:   Solve the equation cos2x= 1 2 .
x=± 2π 3 +πn
x=± π 6 +2πn
x=± π 6 +πn
x=± π 3 +πn
Question 2:   Solve the equations sin x π 6 = 2 2 .
x= 1 n+1 × π 4 + π 6 +πn,nZ
x= 1 n × π 4 + π 6 +πn,nZ
x= 1 n+1 × π 4 π 6 +πn,nZ
x= 1 n+1 × π 4 π 6 +2πn,nZ
Question 3:   Solve the equation tg 2x 3 = 3 .
x= π 3 + 3πn 2 ,nZ
x= π 2 + 3πn 2 ,nZ
x= π 4 + 3πn 2 ,nZ
x= π 2 +πn,nZ
Question 4:   Solve the equation ctg6x=0 .
x= π 6 + πn 6 ,nZ
x= π 12 + πn 6 ,nZ
x= π 12 + πn 12 ,nZ
x= π 12 +πn,nZ
Question 5:   Solve the expression sin arcsin π 3 .
π 6
1 2
π 3
3 2
Question 6:   Solve the expression cos 2arctg 1 3 .
2 3 3
4 5
4 5
11 9
Question 7:   Simplify the expression sin 2 4α cos 2 4α .
cos4α
cos8α
cos8α
1
Question 8:   Simplify the expression cos 2 6β+ sin 2 6β .
cos2β
- cos2β
1
1
Question 9:   Solve the equation sin2x+cosx=0 .
x= 1 n+1 × π 6 +πn,nZ
x 1 = π 2 +πn,nZ x 2 = 1 n+1 × π 6 +πn,nZ
x= π 2 +πn,nZ
Question 10:   Solve the equation tgx+1 cos 2 x =3 .
x 1 =1 x 2 =2
x 1 =1 x 2 =2
0