p¥êÆ7?41.4.2 u¼ê!{u¼ê5 (1) öS‰Y

ìÜ ÆNá¥Æ249

.ÀJK

3π3π

1.A.y=sin(x+π) üN4O«m [2kπ π,2kπ+],k∈Z. k=0 = [ π,].π2.B.k ļêy=log1sin(2x+π) ½Â . ¦sin(2x+)>0,=2kπ<2x+32kπ+π,= kπ<x<kπ+π.q ¦¼ê O¼ê, 2kπ 3πkkπ π≤x≤kπ+π.nþ,¼ê üN~«m (kπ ,kπ

π

<

π≤+π],

2x+

π

≤2kπ+π,=

k∈Z.

3.B.f(x)=cos2x+2asinx 1= sin2x+2asinx= (sinx a)2+a2,Ï0≤x≤2π,

sin 1≤x≤1,…顶a>1,¤±, sinx=1 ,f(x)max= (1 a)2+a2=1 2a.

π5

π) 顶 2x+54.A.y=sin(2x+π=kπ+, x=

kπ

π,k∈Z. k=1 ,

x= π.

5.C.©OxѼêy=sinx ¼êy=lgx ¼êã–,5¿é'…:(1,0),(0,1).6.A.BÀ‘¥ ¼êy=sin|x|´ó¼ê Ø´±Ï¼ê;CÀ‘¥ ¼êy=sin(2x+π)

±Ï π, Ø´ó¼ê;DÀ‘¥ ¼êy=sin(x+π)±Ï 2π.

.

W K

7.f(x)=sin2x cosx. x<0 , x>0,Kf( x)=sin( 2x)+cos( x)= sin2x+cosx,qÏ ¼êf(x) Û¼ê, f( x)= f(x),u´f(x)= f( x)=sin2x cosx.

8.2.f(n)=sinnπ ±Ï T=

2π

=12,Kkf(1)=f(13),f(3)=f(15),f(5)=

1,

5

f(3)=sinπ=1,f(5)=sinπ=

1

,

f(17),......u´f(1)+f(3)+f(5)+......+f(101)=8(f(1)+f(3)+f(5)+f(7)+f(9)+f(11))+f(1)+f(3)+f(5),qÏ f(1)=sinπ=

f(7)=

13111sin7π= ,f(9)=sinπ= 1,f(11)=sinπ= , ª=2.

9.[ 4,4].dcos2x=1 sin2x, § z sin2x 4sinx+a 1=0,q 1≤sinx≤1,

y3¯K8( sinx∈[ 1,1] , §sin2x 4sinx+a 1=0k).=a= sin2x+4sinx+1,¦d m>ù ¼êy= sin2x+4sinx+1 3sinx∈[ 1,1] = .

y= sin2x+4sinx+1= (sinx 2)2+5,sinx∈[ 1,1], sinx= 1 ,ymin= 4,

sinx=1 ,ymax=4,¤±a ‰ [ 4,4].

10.[ 4, π)∪(0,π).dK8 sinx>0…16 x2≥0,=k2kπ<x<2kπ+π,kπZ,

… 4≤x≤4,üö 8k 4≤x< π½0<x<π,d k= 1,0. ¼ê ½Â [ 4, π)∪(0,π).

n.

)‰K