三角比(高一下)1.已知cos(a+b)cosa+sin(a+b)sina=-0.8,求sin(270度+b)2.在三角形ABC中,a,b,c分别为角A,角B,角C的对边,S为三角形ABC的面积,且4sin Bsin^2(45度+B/2)+cos 2B=1+根号3(1)求角B的度数(2)若a=4,s=5根号3,
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/20 16:45:03
![三角比(高一下)1.已知cos(a+b)cosa+sin(a+b)sina=-0.8,求sin(270度+b)2.在三角形ABC中,a,b,c分别为角A,角B,角C的对边,S为三角形ABC的面积,且4sin Bsin^2(45度+B/2)+cos 2B=1+根号3(1)求角B的度数(2)若a=4,s=5根号3,](/uploads/image/z/14469735-39-5.jpg?t=%E4%B8%89%E8%A7%92%E6%AF%94%EF%BC%88%E9%AB%98%E4%B8%80%E4%B8%8B%EF%BC%891.%E5%B7%B2%E7%9F%A5cos%28a%2Bb%29cosa%2Bsin%28a%2Bb%29sina%3D-0.8%2C%E6%B1%82sin%EF%BC%88270%E5%BA%A6%2Bb%292.%E5%9C%A8%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E4%B8%AD%2Ca%2Cb%2Cc%E5%88%86%E5%88%AB%E4%B8%BA%E8%A7%92A%2C%E8%A7%92B%2C%E8%A7%92C%E7%9A%84%E5%AF%B9%E8%BE%B9%2CS%E4%B8%BA%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E7%9A%84%E9%9D%A2%E7%A7%AF%2C%E4%B8%944sin+Bsin%5E2%EF%BC%8845%E5%BA%A6%2BB%2F2%29%2Bcos+2B%3D1%2B%E6%A0%B9%E5%8F%B73%281%29%E6%B1%82%E8%A7%92B%E7%9A%84%E5%BA%A6%E6%95%B0%282%29%E8%8B%A5a%3D4%2Cs%3D5%E6%A0%B9%E5%8F%B73%2C)
三角比(高一下)1.已知cos(a+b)cosa+sin(a+b)sina=-0.8,求sin(270度+b)2.在三角形ABC中,a,b,c分别为角A,角B,角C的对边,S为三角形ABC的面积,且4sin Bsin^2(45度+B/2)+cos 2B=1+根号3(1)求角B的度数(2)若a=4,s=5根号3,
三角比(高一下)
1.已知cos(a+b)cosa+sin(a+b)sina=-0.8,求sin(270度+b)
2.在三角形ABC中,a,b,c分别为角A,角B,角C的对边,S为三角形ABC的面积,且4sin Bsin^2(45度+B/2)+cos 2B=1+根号3
(1)求角B的度数
(2)若a=4,s=5根号3,求b的值]
三角比(高一下)1.已知cos(a+b)cosa+sin(a+b)sina=-0.8,求sin(270度+b)2.在三角形ABC中,a,b,c分别为角A,角B,角C的对边,S为三角形ABC的面积,且4sin Bsin^2(45度+B/2)+cos 2B=1+根号3(1)求角B的度数(2)若a=4,s=5根号3,
(1)cos(a+b)cosa+sin(a+b)sina=-0.8
cos(a+b-a)=-0.8=cosb
sin(270+b)=-sin(90+b)=-cosb
因为cosb=-0.8
所以-cosb=0.8
(2)4sinbsin^2(45+B/2)+cos(2B)=1+√3
首先我们先处理sin^2(45+b/2)
sin^2(45+b/2)=1/2*(sinb/2+cosb/2)^2
=1/2*(sin^2(b/2)+cos^2(b/2)+2cosb/2*sin(b/2))
=1/2*(1+2cosb/2*sin*b/2)
因为有公式:sin(a)cos(b)=1/2*[sin(a+b)+sin(a-b)]
所以
=1/2*(1+2*1/2*(sinb))
=1/2*(1+sinb)
=1/2+1/2*sinb
化简原式=4*sinb*1/2(1+sinb)+(1-2sin^b)=1+√3
=2sinb*(1+sinb)+1-2sin^2b=1+√3
=2sin^2b+2sinb-2sin^2b=√3
sinb=√3/2
所以b=60度
(3)a=4,s=5√3
s=1/2*a*c*sinb
5√3=1/2*4*c*√3/2
c=5
所以a=4 b=5
利用余弦定理
2ac*cos(60)=a^2+c^2-b^2
所以
b^2=a^2+c^2-2ac*1/2
=a^2+c^2-ac
=16+25-20=21
b=√21