题目
1.已知sin(π/4-α)=3/5,π/4-α为第二象限角,求sin(α-13π/4)+sin(α+21π/4)的值
2.已知y=a-bcos(3x-π/2的最大值为6,最小值为-2,求实数a,b的值
2.已知y=a-bcos(3x-π/2的最大值为6,最小值为-2,求实数a,b的值
提问时间:2020-12-06
答案
1
sin(π/4-α)=3/5
π/4-α为第二象限角
cos(π/4-α)=-根号[1-sin^2(π/4-α)]=-根号[1-(3/5)^2] = -4/5
sin(α-13π/4)+sin(α+21π/4)
=sin(-4π+π+α-π/4)+sin(4π+π+α+π/4)
=sin(π+α-π/4)+sin(π+α+π/4)
=-sin(α-π/4)-sin(α+π/4)
=sin(π/4-α)-cos(π/2-α-π/4)
=sin(π/4-α)-cos(π/4-α)
=3/5-(-4/5)
=8/5
2.
y=a-bcos(3x-π/2)
-1≤ cos(3x-π/2) ≤ 1
当b>0时:
最小值a-b=-2,最大值a+b=6
a=2,b=4
当b<0时:
最小值a+b=-2,最大值a-b=6
a=2,b=-4
sin(π/4-α)=3/5
π/4-α为第二象限角
cos(π/4-α)=-根号[1-sin^2(π/4-α)]=-根号[1-(3/5)^2] = -4/5
sin(α-13π/4)+sin(α+21π/4)
=sin(-4π+π+α-π/4)+sin(4π+π+α+π/4)
=sin(π+α-π/4)+sin(π+α+π/4)
=-sin(α-π/4)-sin(α+π/4)
=sin(π/4-α)-cos(π/2-α-π/4)
=sin(π/4-α)-cos(π/4-α)
=3/5-(-4/5)
=8/5
2.
y=a-bcos(3x-π/2)
-1≤ cos(3x-π/2) ≤ 1
当b>0时:
最小值a-b=-2,最大值a+b=6
a=2,b=4
当b<0时:
最小值a+b=-2,最大值a-b=6
a=2,b=-4
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