Question

已知O為坐標(biāo)原點(diǎn),  =(2asin²x,a), =(1,-2sinxcos x+1),F(x)= ·+b(a＜b且 a≠0),?

(1)求y=F(x)的單調(diào)遞增區(qū)間;

(2)若F(x)的定義域?yàn)椋?IMG align="middle" height=41 src="http://thumb.zyjl.cn/pic1/1898/img/06/71/28/189806712810005728/6.gif" width=17 align=absMiddle v:shapes="_x0000_i1198">,π］,值域?yàn)椋郏�，５］，�?I >a,b的值.

Answer 1

解:(1)f(x)= ·+b

=2asin²x-2asinxcosx+a+b??

=a(1-cos2x)-asin2x+a+b?

=-2asin(2x+)+2a+b.                                                                                      ?

a＞0時(shí),由2kπ+≤2x+≤2kπ+(k∈Z),得y=f(x)的單調(diào)遞增區(qū)間為［kπ+,kπ+ ］(k∈Z);                                                                                                       ?

a＜0時(shí),由2kπ-≤2x+≤2kπ+ (k∈Z),得

y=f(x)的單調(diào)遞增區(qū)間為［kπ-,kπ+］(k∈Z).?                                         ?

(2)f(x)=-2asin(2x+)+2a+b,?

x∈［,π］,2x+∈［,］,?

sin(2x+)∈［-1, ］.                                                                           ?

a＞0時(shí),得?

不滿足a＜b,舍.                                                                                                      ?

a＜0時(shí),得                                                            ?

綜上,a=-1,b=6.