高考数学复习回扣4三角函数与平面向量理市赛课公开课一等奖省名师优质课获奖PPT课件.pptx

回扣,4,三角函数与平面向量,考前回扣,1/54,基础回归,易错提醒,回归训练,2/54,基础回归,3/54,1.,准确记忆六组诱导公式,对于,“,，,k,Z,”,三角函数值与,角三角函数值关系口诀：奇变偶不变，符号看象限,.,2.,三角函数恒等变换,“,四大策略,”,(1),常值代换：尤其是,“,1,”,代换，,1,sin,2,cos,2,tan 45,等,.,(2),降次与升次：正用二倍角公式升次，逆用二倍角公式降次,.,(3),弦、切互化：普通是切化弦,.,4/54,3.,三种三角函数性质,函数,y,sin,x,y,cos,x,y,tan,x,图象,5/54,6/54,7/54,4.,函数,y,A,sin(,x,)(,0,，,A,0),图象,(1),“,五点法,”,作图,(2),由三角函数图象确定解析式时，普通利用五点中零点或最值点作为解题突破口,.,8/54,(3),图象变换,9/54,10/54,11/54,8.,平面向量数量积,(1),若,a,，,b,为非零向量，夹角为,，则,ab,|,a|b,|cos,.,(2),设,a,(,x,1,，,y,1,),，,b,(,x,2,，,y,2,),，则,ab,x,1,x,2,y,1,y,2,.,9.,两个非零向量平行、垂直充要条件,若,a,(,x,1,，,y,1,),，,b,(,x,2,，,y,2,),，则,(1),a,b,a,b,(,b,0,),x,1,y,2,x,2,y,1,0.,(2),a,b,ab,0,x,1,x,2,y,1,y,2,0.,12/54,13/54,12.,三角形,“,四心,”,向量形式充要条件,设,O,为,ABC,所在平面上一点，角,A,，,B,，,C,所正确边长分别为,a,，,b,，,c,，则,14/54,易错提醒,15/54,1.,利用同角三角函数平方关系式求值时，不要忽略角范围，要先判断函数值符号,.,2.,在求三角函数值域,(,或最值,),时，不要忽略,x,取值范围,.,3.,求函数,f,(,x,),A,sin(,x,),单调区间时，要注意,A,与,符号，当,0,时，需把,符号化为正值后求解,.,4.,三角函数图象变换中，注意由,y,sin,x,图象变换得到,y,sin(,x,),时，平移量为,，而不是,.,16/54,5.,在已知两边和其中一边对角时，要注意检验解是否满足,“,大边对大角,”,，防止增解,.,6.,要尤其注意零向量带来问题：,0,模是,0,，方向任意，并不是没有方向；,0,与任意非零向量平行,.,7.,ab,0,是,a,，,b,为锐角必要不充分条件；,ab,0,是,a,，,b,为钝角必要不充分条件,.,17/54,III,回归训练,18/54,答案,解析,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,19/54,答案,解析,2.,以下函数中，最小正周期为,偶函数是,解析,化简函数解析式，,A,中，,y,cos 2,x,是最小正周期为,偶函数,.,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,20/54,答案,解析,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,解得,b,1,，故选,A.,21/54,答案,解析,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,22/54,答案,解析,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,23/54,1,2,3,4,5,6,7,8,9,10,11,1213,14,15,16,24/54,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,25/54,解析,设,BC,边上高,AD,交,BC,于点,D,，,答案,解析,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,26/54,答案,解析,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,27/54,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,sin(,),sin,(,),2,sin(,)cos 2,cos(,)sin 2,28/54,cos(,),cos,(,),2,cos()cos 2,sin(,)sin 2,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,29/54,答案,解析,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,30/54,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,解析,如图，,31/54,答案,解析,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,32/54,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,33/54,答案,解析,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,34/54,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,35/54,答案,解析,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,36/54,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,37/54,答案,解析,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,38/54,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,解析,由两个三角函数图象对称中心完全相同可知，两函数周期相同，故,2,，,39/54,答案,解析,1,23,4,5,6,7,8,9,10,11,12,13,14,15,16,13.,在,ABC,中，内角,A,，,B,，,C,对边分别是,a,，,b,，,c,，角,B,为锐角，且,sin,2,B,8sin,A,sin,C,，则,取值范围为,_.,40/54,解析,因为,sin,2,B,8sin,A,sin,C,，由正弦定理可知，,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,41/54,答案,解析,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,42/54,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,设ABC,三个内角,A,，,B,，,C,所正确边分别为,a,，,b,，,c,，,43/54,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,所以,b,2,R,sin,B,，,c,2,R,sin,C,，,44/54,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,代入上式整理，得,cos,B,cos,C,cos,A,m,sin,C,，,45/54,解答,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,(1),求角,B,大小；,46/54,解答,1,2,3,4,5,6,7,8,9,10,11,12,13,1415,16,(2),若,a,2,，,b,，求,ABC,面积,.,47/54,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,48/54,解答,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,49/54,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,50/54,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,51/54,解答,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,(2),设,ABC,内角,A,，,B,，,C,所正确边分别为,a,，,b,，,c,，且,c,，,f,(,C,),2,，若向量,m,(1,，,a,),与向量,n,(2,，,b,),共线，求,a,，,b,值,.,52/54,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,向量,m,(1,，,a,),与向量,n,(2,，,b,),共线，,b,2,a,0,，即,b,2,a,.,53/54,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,即,a,2,b,2,ab,3.,由,得,a,1,，,b,2.,54/54,