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正、餘弦函數的疊合

正、餘弦函數的疊合. 正、餘弦函數的疊合. 正弦函數 y=sinx 餘弦函數 y=cosx. 正、餘弦函數的疊合. y=sinx+cosx 稱為正、餘弦函數的疊合 若 y=sinx+cosx =rsin(x+ Ө ),r>0 求 r=? Ө =?. 正、餘弦函數的疊合.

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正、餘弦函數的疊合

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  1. 正、餘弦函數的疊合

  2. 正、餘弦函數的疊合 • 正弦函數 y=sinx • 餘弦函數 y=cosx

  3. 正、餘弦函數的疊合 • y=sinx+cosx稱為正、餘弦函數的疊合 • 若y=sinx+cosx =rsin(x+Ө),r>0求 r=? Ө =?

  4. 正、餘弦函數的疊合 • 若y=sinx+cosx = rsin(x+Ө),r>0,求 r=? Ө =?因為y=sinx+cosx = rsin(x+Ө) =r(sinx‧cosӨ+cosx‧sinӨ)又 y=1‧sinx+1‧cosx = ( ‧sinx+ ‧cosx ) = (sinx‧cos +cosx‧sin ) = sin(x+ ) 所以r= Ө =

  5. 正、餘弦函數的疊合 • 推廣y=a‧sinx+b‧cosx稱為正、餘弦函數的疊合 • y=a‧sinx+b‧cosx= sin(x+ Ө )

  6. 正、餘弦函數的疊合 • 再推廣y=a‧sinx+b‧cosx稱為正、餘弦函數的疊合 • y=a‧sinx+b‧cosx= cos(x- Ө )

  7. 正、餘弦函數的疊合 • 若y=sinx+cosx = rcos(x+Ө),r>0,求 r=? Ө =?因為y=sinx+cosx = rcos(x- Ө) =r(cosx‧cosӨ+sinx‧sinӨ)又 y=1‧sinx+1‧cosx = ( ‧sinx+ ‧cosx ) = (cosx‧cos +sinx‧sin ) = cos(x- ) 所以r= , Ө =

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