急求三角函数cos10°cos50°cos70°的值.
来源：学生作业帮助网 编辑：六六作业网 时间：2024/11/26 12:17:26
急求三角函数cos10°cos50°cos70°的值.
急求三角函数cos10°cos50°cos70°的值.
急求三角函数cos10°cos50°cos70°的值.
用积化和差做
cos10°cos50°cos70°
=0.5*{cos(10°+50°)+cos(10°-50°)}*cos70°
=0.5(cos60°+cos40°)cos70°
=0.5(0.5+cos40°)cos70°
=0.25*cos70°+0.5*cos40°cos70°
=0.25*cos70°+0.5*0.5{cos(40°+70°)+cos(40°-70°)}
=0.25*cos70°+0.25[cos110°+cos30°]
=0.25(cos70°+cos110°+cos30°)
因为cos70°=cos(180°-110°)=-cos110°
所以cos70°+cos110°＝0
所以原式=0.25*cos30°=八分之根号三
分别为0.984,0.642,0.342
cos10°cos50°cos70°
=1/2*{cos(10°+50°)+cos(10°-50°)}*cos70°
=1/2(cos60°+cos40°)cos70°
=1/2(1/2+cos40°)cos70°
=1/4*cos70°+1/2*cos40°cos70°
=1/4*cos70°+1/2*1/2{cos(40°+70°)+cos(40°-70...
全部展开
cos10°cos50°cos70°
=1/2*{cos(10°+50°)+cos(10°-50°)}*cos70°
=1/2(cos60°+cos40°)cos70°
=1/2(1/2+cos40°)cos70°
=1/4*cos70°+1/2*cos40°cos70°
=1/4*cos70°+1/2*1/2{cos(40°+70°)+cos(40°-70°)}
=1/4*cos70°+1/4[cos110°+cos30°]
=1/4(cos70°+cos110°+cos30°)
=1/4[cos(180-110°)+cos110°+cos30°]
=1/4[-cos110°+cos110°+cos30°]
=1/4*cos30°
=1/4*√3/2
=√3/8
收起