已知y=cos(2x-π/12)sin(2x+π/4)。
(a)若y=asin(4x+π/6)+b,其中a,b為常數,試求a和b的值。
(b)試求y我極大值和極小值。
a-maths!!!!!!
2007-08-12 4:53 am
回答 (1)
2007-08-12 6:16 am
✔ 最佳答案
a)y = cos(2x-π/12)sin(2x+π/4)= sin (2x+π/4) cos (2x-π/12)
= ( 1 / 2 ) sin (2x+π/4 +2x-π/12) + ( 1 / 2 ) sin (2x+π/4 -2x +π/12)
= ( 1 / 2 ) sin (4x+π/6) + ( 1 / 2 ) sin (π/ 3 )
所以, a = 1 / 2 , b = √3 / 4
b)極大值: ( 1 / 2 )( 1 ) + √3 / 4 = ( 2 + √3) / 4 ( 當sin (4x+π/6) = 1 )
極小值: ( 1 / 2 )( - 1 ) + √3 / 4 = ( - 2 + √3) / 4 ( 當sin (4x+π/6) = - 1 )
參考: My Maths Knowledge
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