算道高三数学三角函数题若Cos(2X+a+π(pai)/3)是偶函数,则a角为多少?解法1:Cos(2X+a+π/3)是偶函数 因为Cos(2X+Kπ)=-cos(2X)余弦函数是偶函数,所以a+π/3=Kπ a=Kπ-π/3解法2:Cos(2X+a+π/3)是偶函数 则Cos(2X+a+π/3)=Cos(-2X+a+π/3)=Cos(-2X+a+2Kπ) a+π/3=2Kπa=2Kπ-π/3哪个是正确的?解说下
2020-04-29
算道高三数学三角函数题
若Cos(2X+a+π(pai)/3)是偶函数,则a角为多少?
解法1:Cos(2X+a+π/3)是偶函数 因为Cos(2X+Kπ)=-cos(2X)余弦函数是偶函数,所以a+π/3=Kπ a=Kπ-π/3
解法2:Cos(2X+a+π/3)是偶函数 则Cos(2X+a+π/3)=Cos(-2X+a+π/3)=Cos(-2X+a+2Kπ) a+π/3=2Kπ
a=2Kπ-π/3
哪个是正确的?解说下
优质解答
Cos(2X+a+π/3)=Cos(-2X+a+π/3)
Cos(-2X+a+π/3)=Cos[-(2X-a-π/3)]=Cos(2X-a-π/3)
Cos(2X-a-π/3)=Cos(2X+a+π/3)
2X-a-π/3=2X+a+π/3
2a=-2π/3
a=-π/3
Cos(2X+a+π/3)=Cos(-2X+a+π/3)
Cos(-2X+a+π/3)=Cos[-(2X-a-π/3)]=Cos(2X-a-π/3)
Cos(2X-a-π/3)=Cos(2X+a+π/3)
2X-a-π/3=2X+a+π/3
2a=-2π/3
a=-π/3