Question

已知三角形ABC,BC=1,∠A=120°,∠B=θ既f(θ)=向量BA乘以向量AC 求 f(θ)关于θ的表达式 求f(

Answer 1

f(θ)=BA·AC=-AB·AC=bc/2

b/sinθ=c/sin(π/3-θ)=1/sinA

即：b=2sinθ/√3,c=2sin(π/3-θ)/√3

故：f(θ)=2sinθsin(π/3-θ)/3

2

f(θ)=2sinθsin(π/3-θ)/3

=(2/3)(-1/2)(cos(π/3)-cos(2θ-π/3))

=(-1/3)(1/2-cos(2θ-π/3))

=(1/3)cos(2θ-π/3)-1/6

0