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cos(10t)-cos(30t)的周期T
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cos(10t)-cos(30t) 的周期T
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答案和解析
f(t)=cos(10t)+cos(30t)
=cos(10t)+cos(10t)cos(20t)-sin(10t)sin(20t)
=cos(10t)+cos(10t)*[2cos(10t)^2-1]-2cos(10t)*sin(10t)^2
=2cos(10t)*[2cos(10t)^2-1]
=4cos(10t)^3-2cos(10t)
因为y=cos(t)的周期为2π
所以y=cos(10t)的周期为2π/10=π/5
f(t)=4cos(10t)^3-2cos(10t)的周期也是π/5
=cos(10t)+cos(10t)cos(20t)-sin(10t)sin(20t)
=cos(10t)+cos(10t)*[2cos(10t)^2-1]-2cos(10t)*sin(10t)^2
=2cos(10t)*[2cos(10t)^2-1]
=4cos(10t)^3-2cos(10t)
因为y=cos(t)的周期为2π
所以y=cos(10t)的周期为2π/10=π/5
f(t)=4cos(10t)^3-2cos(10t)的周期也是π/5
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