已知向量a=(sin c,1),b=(1,cos c),-π/2<c<π/2(1)若a⊥b,求c(c为角名称)(2)求|a+b|的最大值
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已知向量a=(sin c,1),b=(1,cos c),-π/2<c<π/2(1)若a⊥b,求c(c为角名称)(2)求|a+b|的最大值
已知向量a=(sin c,1),b=(1,cos c),-π/2<c<π/2
(1)若a⊥b,求c(c为角名称)
(2)求|a+b|的最大值
已知向量a=(sin c,1),b=(1,cos c),-π/2<c<π/2(1)若a⊥b,求c(c为角名称)(2)求|a+b|的最大值
(1)
若a⊥b,a.b=0,sinc+cosc=0
=> sin(c+π/4)=0
=> c+π/4=kπ,(k是整数)
=>c=kπ-π/4
而-π/2<c<π/2
=>c=-π/4 (k取0时)
(2)
a+b=(sinc+1,1+cosc)
|a+b|^2=(sinc+1)^2+(cosc+1)^2=3+2(sinc+cosc)=3+2√2sin(c+π/4)
看其中的 sin(c+π/4),c的范围是 -π/2<c<π/2
那么 c+π/4 的范围是 -π/4