已知直线y等于二分之一与函数y等于2sin(x+4分之派)cos(4分之派-x)的图像,在y轴右侧的交点的横坐标自左向右依次记为x1,x2,x3,x4,……,xn.则x1+x2+x3+x4,等于.
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![已知直线y等于二分之一与函数y等于2sin(x+4分之派)cos(4分之派-x)的图像,在y轴右侧的交点的横坐标自左向右依次记为x1,x2,x3,x4,……,xn.则x1+x2+x3+x4,等于.](/uploads/image/z/2581804-28-4.jpg?t=%E5%B7%B2%E7%9F%A5%E7%9B%B4%E7%BA%BFy%E7%AD%89%E4%BA%8E%E4%BA%8C%E5%88%86%E4%B9%8B%E4%B8%80%E4%B8%8E%E5%87%BD%E6%95%B0y%E7%AD%89%E4%BA%8E2sin%28x%2B4%E5%88%86%E4%B9%8B%E6%B4%BE%29cos%284%E5%88%86%E4%B9%8B%E6%B4%BE-x%29%E7%9A%84%E5%9B%BE%E5%83%8F%2C%E5%9C%A8y%E8%BD%B4%E5%8F%B3%E4%BE%A7%E7%9A%84%E4%BA%A4%E7%82%B9%E7%9A%84%E6%A8%AA%E5%9D%90%E6%A0%87%E8%87%AA%E5%B7%A6%E5%90%91%E5%8F%B3%E4%BE%9D%E6%AC%A1%E8%AE%B0%E4%B8%BAx1%2Cx2%2Cx3%2Cx4%2C%E2%80%A6%E2%80%A6%2Cxn.%E5%88%99x1%2Bx2%2Bx3%2Bx4%2C%E7%AD%89%E4%BA%8E.)
已知直线y等于二分之一与函数y等于2sin(x+4分之派)cos(4分之派-x)的图像,在y轴右侧的交点的横坐标自左向右依次记为x1,x2,x3,x4,……,xn.则x1+x2+x3+x4,等于.
已知直线y等于二分之一与函数y等于2sin(x+4分之派)cos(4分之派-x)的图像,在y轴右侧的交点的横坐标自左向右依次记为x1,x2,x3,x4,……,xn.则x1+x2
+x3+x4,等于.
已知直线y等于二分之一与函数y等于2sin(x+4分之派)cos(4分之派-x)的图像,在y轴右侧的交点的横坐标自左向右依次记为x1,x2,x3,x4,……,xn.则x1+x2+x3+x4,等于.
函数1:
y = 1/2
函数2:
y = 2sin(x + π/4)cos(π/4 - x) = 2sin(x + π/4)cos(π/2 - (x + π/4)) = 2sin(x + π/4)sin(x + π/4)
两者的交点就是2sin(x + π/4)sin(x + π/4) = 1/2
sin(x+ π/4) = 1/2 或者 -1/2
x + π/4 = kπ + 30° 或者x + π/4 = kπ - 30°,其中k为整数
也就是
x + π/4 = kπ + π/6或者x + π/4 = kπ - π/6
x = kπ - π/12 或者x = kπ - 5π/12
由于交点位于y轴右侧,因此x > 0
所以x1 = 7π/12,x2 = 11π/12,x3 = 19π/12,x4 = 23π/12°
x1 + x2 + x3 + x4 = 7π/12+ 11π/12 + 19π/12 + 23π/12= 60π/12 = 5π
已知直线Y=1/2与函数Y=2sin(x+π/4)cos(π/4-x)的图像在Y轴右侧的交点的横坐标自左向右依次为X1,X2,X3,X4……Xn……则X1+X2+X3+X4=?
Y=2sin(x+π/4)cos(π/4-x)=2sin(x+π/4)sin(π/4+x)=1-cos(2x+π/2)=1-sin(-2x)=1+sin2x
当2x=7π/6,11π/6,19π/6,23π...
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已知直线Y=1/2与函数Y=2sin(x+π/4)cos(π/4-x)的图像在Y轴右侧的交点的横坐标自左向右依次为X1,X2,X3,X4……Xn……则X1+X2+X3+X4=?
Y=2sin(x+π/4)cos(π/4-x)=2sin(x+π/4)sin(π/4+x)=1-cos(2x+π/2)=1-sin(-2x)=1+sin2x
当2x=7π/6,11π/6,19π/6,23π/6,。。。时sin2x=-1/2,Y=1/2
X1+X2+X3+X4=(7π/6+11π/6+19π/6+23π/6)/2=5π
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