高一三角函数1~函数y=sin(
y=sin(3x+60)cos(x-30)+cos(3x+60)cos(x+60)
=(1/2)[sin(3x+60+x-30)+sin(3x+60-x+30)]+(1/2)[cos(3x+60+x+60)+cos(3x+60-x-60)]
=(1/2)[sin(4x+30)+sin(2x+90)]+(1/2)[cos(4x+120)+cos2x]
=(1/2)[sin(4x+30)+cos2x]+(1/2)[-sin(4x+30)+cos2x]
=cos2x+(1/2)[sin(4x+30)-sin(4x+30)]
=cos2x+0
=cos2x
很明显,其对称轴x=kπ/2 (k为整数...全部
y=sin(3x+60)cos(x-30)+cos(3x+60)cos(x+60)
=(1/2)[sin(3x+60+x-30)+sin(3x+60-x+30)]+(1/2)[cos(3x+60+x+60)+cos(3x+60-x-60)]
=(1/2)[sin(4x+30)+sin(2x+90)]+(1/2)[cos(4x+120)+cos2x]
=(1/2)[sin(4x+30)+cos2x]+(1/2)[-sin(4x+30)+cos2x]
=cos2x+(1/2)[sin(4x+30)-sin(4x+30)]
=cos2x+0
=cos2x
很明显,其对称轴x=kπ/2 (k为整数)
选D
第2小题:
①题目要求:
向右平移60度个单位 y'=f(x-60°)
横坐标变为原来的2倍 y''=f[(x-60°)/2]
②你的方法:
横坐标变为原来的1/2, y'=cos2x
沿x轴向左平移60度个单位 y''=cos(2x+60°)
你自己比较一下区别
。
收起