函数f(x)=
（I）求φ的值； （Ⅱ）将函数y=f（x）的图象上各点的横坐标缩短到原来的
|
（1）由条件知
=1 2
sinφ+3 4
cosφ=1 4
sin(φ+1 2
)π 6
∴φ+
=π 6
⇒φ=π 2 π 3
（2）由（1）代入得f(x)=
sin2x1 2
+cos2x3 2
-1 2
cosφ1 2
=
sin2x1 2
+3 2 1+cos2x 2
-1 2
=1 4
sin(2x+1 2
)π 6
∴函数g（x）=
sin(4x+1 2
)π 6
∴函数y=g（x）的周期为T=π 2
递减区间为[
+π 12
kπ，1 2
+π 3
kπ]1 2 &(k∈Z)
| 完形填空 | ||||
There are about fifteen hundred languages in the worl d. But 1 a few of them are very 2 . English is one of these. Many, many people use it, not only in England and the U.S.A., but in other parts of the world. About 200,000,000 speak it as their own language. It is difficult to say how many people are learning it as a 3 language. Many millions are 4 to do so. Is it easy or difficult to learn English? Different people may have different 5 . Have you ever 6 ads( 广告) of this kind in the newspapers or magazines? "Learn English in six weeks, or your 7 back..." "Easy and funny! Our records and tapes 8 you master your English in a month. 9 the first day your 10 will be excellent. Just send ... " Of course, it never 11 quite like this.The only language that seems easy to learn is the mother tongue. We should 12 that we all learned our own language well when we were 13 . If we could learn English in the same way, it would not seem so difficult. 14 what a small child does. He listens to what people say. He tries what he hears. When he is using the language, talking in it, 15 in it all the time. Just imagine how much 6 that gets! So it is 17 to say that learning English is easy, because a go  od command of English 18 upon a lot of practice. And practice needs great effort and 19 much time. Good teachers, records, tapes, books, and dictionaries will 20 . But they cannot do the student's work for him. | ||||
|