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1.若cos31°=a,则sin211°=2.cos(π+π/3)cos(2π+π/3)cos(3π+π/3).cos(100π+π/3)3.已知cos(75°+a)=1/3,且a是第三象限角,求cos(105°-a)+sin(a-105°)的值
题目详情
1.若cos31°=a,则sin211°=
2.cos(π+π/3)cos(2π+π/3)cos(3π+π/3).cos(100π+π/3)
3.已知cos(75°+a)=1/3,且a是第三象限角,求cos(105°-a)+sin(a-105°)的值
2.cos(π+π/3)cos(2π+π/3)cos(3π+π/3).cos(100π+π/3)
3.已知cos(75°+a)=1/3,且a是第三象限角,求cos(105°-a)+sin(a-105°)的值
▼优质解答
答案和解析
1.sin211°=sin(π+31°)=-sin31°=-√(1-cos²31°)=-√(1-a²)
2.cos(π+π/3)cos(2π+π/3)cos(3π+π/3).cos(100π+π/3)
=-cos(π/3)cos(π/3)······cos(π/3)
=-1/2的100次方
3.cos(105°-a)=cos(π-(75°+a))=-cos(75°+a)=-1/3
∴105°-a为第二或三象限角
∵a是第三象限角
∴105°-a为第三或第四象限角
∴105°-a为第三象限角
∴sin(a-105°)=-sin(105°-a)=√(1-cos²(105°-a))=√(1-1/9)=2√2/3
∴cos(105°-a)+sin(a-105°)=-1/3+2√2/3=(2√2-1)/3
2.cos(π+π/3)cos(2π+π/3)cos(3π+π/3).cos(100π+π/3)
=-cos(π/3)cos(π/3)······cos(π/3)
=-1/2的100次方
3.cos(105°-a)=cos(π-(75°+a))=-cos(75°+a)=-1/3
∴105°-a为第二或三象限角
∵a是第三象限角
∴105°-a为第三或第四象限角
∴105°-a为第三象限角
∴sin(a-105°)=-sin(105°-a)=√(1-cos²(105°-a))=√(1-1/9)=2√2/3
∴cos(105°-a)+sin(a-105°)=-1/3+2√2/3=(2√2-1)/3
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