三角函数f(x)=sin(2x+π/4)+cos(2x+π/4)怎么化?答案是√2sin(2x+π/4+π/4)=√2sin(2x+π/2)=√2cos2x; 这是根据什么公式得来的?
来源:学生作业帮助网 编辑:作业帮 时间:2024/09/06 04:54:39
![三角函数f(x)=sin(2x+π/4)+cos(2x+π/4)怎么化?答案是√2sin(2x+π/4+π/4)=√2sin(2x+π/2)=√2cos2x; 这是根据什么公式得来的?](/uploads/image/z/2625177-57-7.jpg?t=%E4%B8%89%E8%A7%92%E5%87%BD%E6%95%B0f%28x%29%3Dsin%282x%2B%CF%80%2F4%29%2Bcos%282x%2B%CF%80%2F4%29%E6%80%8E%E4%B9%88%E5%8C%96%3F%E7%AD%94%E6%A1%88%E6%98%AF%E2%88%9A2sin%282x%2B%CF%80%2F4%2B%CF%80%2F4%29%3D%E2%88%9A2sin%282x%2B%CF%80%2F2%29%3D%E2%88%9A2cos2x%3B+%E8%BF%99%E6%98%AF%E6%A0%B9%E6%8D%AE%E4%BB%80%E4%B9%88%E5%85%AC%E5%BC%8F%E5%BE%97%E6%9D%A5%E7%9A%84%3F)
三角函数f(x)=sin(2x+π/4)+cos(2x+π/4)怎么化?答案是√2sin(2x+π/4+π/4)=√2sin(2x+π/2)=√2cos2x; 这是根据什么公式得来的?
三角函数f(x)=sin(2x+π/4)+cos(2x+π/4)怎么化?
答案是√2sin(2x+π/4+π/4)=√2sin(2x+π/2)=√2cos2x;
这是根据什么公式得来的?
三角函数f(x)=sin(2x+π/4)+cos(2x+π/4)怎么化?答案是√2sin(2x+π/4+π/4)=√2sin(2x+π/2)=√2cos2x; 这是根据什么公式得来的?
f(x)=√2(√2/2sin(2x+π/4)+√2/2cos(2x+π/4))=√2(cos(π/4)sin(2x+π/4)+sin(π/4)cos(2x+π/4))==√2sin(2x+π/2)=√2cos2x
是根据公式:asinx+bcosx=√ (a^2+b^2)sin (x+θ),其中sinθ=b/ √(a^2+b^2) ,
cosθ=a/ √(a^2+b^2)
两角和公式:SinA*CosB+CosA*SinB=Sin(A+B)
因为 Sin(π/4)=Cos(π/4)=√2/2
所以 sin(2x+π/4)+cos(2x+π/4)=√2*[√2/2*sin(2x+π/4)+√2/2*cos(2x+π/4)]
=√2*[ Cos(π/4)*sin(2x+π/4)+Sin(π/4)*cos(2x+π/4)]=√2sin(2x+π/4+π/4)
f(x)=sin(2x+π/4)+cos(2x+π/4)=sin2xcosπ/4+cos2xsinπ/4-cos2xcosπ/4-sin2xsinπ/4
=√2cos2x