sin(2x+π/3)- 根号3/2对称轴怎么求,公式是什么
答案是π/12啊,y=sinxcosx+√3cos^2x-√3求这个的对称轴,为什么要k=0?
ããsin(2x+Ï/3)- æ ¹å·3/2对称轴æä¹æ±ï¼æ¹æ³æ¯ä»ä¹ï¼ä¸ºä»ä¹è¦k=0ï¼
ããæ¹æ³ï¼æ¢å æ³ã
ãã令2x+Ï/3=X
ããå¯åæªç¥
ããy=sin(2x+Ï/3)- â3/2ç对称轴æ¹ç¨ï¼
ãã为已ç¥
ããy=sinXç对称轴æ¹ç¨ã
ããç±y=sinXç对称轴æ¹ç¨ä¸ºï¼
ããX=kÏ+Ï/2
ããå¾
ããy=sinX- â3/2ã
ããç对称轴æ¹ç¨ä¸ºï¼
ããX=kÏ+Ï/2ï¼
ããï¼æ³¨ï¼åå»â3/2ï¼åªéå°y=sinXçå¾ååä¸å¹³ç§»â3/2ï¼å¯å¾y=sinX- â3/2çå¾åï¼å¯¹ç§°è½´ä¸åå½±åï¼
ããä»è
ããy=sin(2x+Ï/3)- â3/2
ããç对称轴æ¹ç¨ä¸ºï¼
ããX=kÏ+Ï/2ï¼kâZ.
ãã解ï¼ä»¤2x+Ï/3=X
ããå
ããy=sin(2x+Ï/3)- â3/2
ãã=sinX- â3/2
ããåÏ=2ï¼
ããå¾å¨æ
ããT=2Ï/Ï=2Ï/2=Ïã
ããæ å ¶å¯¹ç§°è½´æ¹ç¨ä¸ºï¼
ããX=kÏ+Ï/2
kâZ.
ããç±
ãã2x+Ï/3=X
ããå¾
ãã2x+Ï/3=kÏ+Ï/2
2x=kÏ+Ï/6
x=kÏ/2+Ï/12ã
ããkåä¸åçæ´æ°ï¼
ããå¾ç¸åºç对称轴æ¹ç¨ã
ããå¦å¾
ããå½k=0æ¶ï¼
ãã对称轴æ¹ç¨ä¸ºï¼x=Ï/12.
ããï¼ç®åä¸ææ±ï¼æ é常åk=0ï¼
ããy=sinxcosx+â3cos^2x-â3æ±è¿ä¸ªç对称轴
ãã解ï¼ç±y=sinxcosx+â3cos^2x-â3
ãã=2sinxcosx/2+(â3/2)2cos^2x-â3
ãã=(1/2)sin2x+(â3/2)(cos2x+1)-â3
ãã=(1/2)sin2x+(â3/2)cos2x+â3/2-â3
ãã=(1/2)sin2x+(â3/2)cos2x-â3/2
ãã=sin(2x-Ï/3)-â3/2.
ãã仿ä¸æ³å¾
ãã2x-Ï/3=kÏ+Ï/2
2x=kÏ+5Ï/6
x=kÏ/2+5Ï/12
ãã对称轴æ¹ç¨ä¸ºï¼
ããx=kÏ/2+5Ï/12
ããkâZ.
ããå½k=0æ¶ï¼
ãã对åºç对称轴æ¹ç¨ä¸ºï¼x=5Ï/12.