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sin(1/2ArCsin3/5)

设arcsin1/3=x,即sinx=1/3. sin2arcsin1/3=sin2x =2sinxcosx 由sinx2+cosx2=1解得cosx=正负3分之2倍根号2 所以sin2x=2sinxcosx=正负9分之4倍根号2

sin(arcsin1/2+arccos1/3) =sin(arcsin1/2)cos(arccos1/3)+cos(arcsin1/2)sin(arccos1/3) =1/2*1/3+根号(1-(1/2)^2)*根号(1-(1/3)^2) =1/6+(根号3)/2*2根号(2)/3 =1/6+(根号6)/3 =(1+2根号6)/6

令sinX = 3/5,X=arcsin(3/5),则cosX=±4/5 sin[2arcsin(3/5)]=sin2X=2sinXcosX=2x(3/5)x(±4/5)=±24/25

arcsinx为反正弦,定义域在[-1,1],单调递增 值域在[-π/2,π/2]上 求arcsin1/2,就是看在[-π/2,π/2]上谁的正弦等于1/2 sin(π/6)=1/2,所以arc sin 1/2=π/6 (=30°) 同理arcsin(-1/2)=-π/6(=-30°) 函数y=sinx,x∈[-π/2,π/2]的反函数叫做反正...

设a=arcsin1/3 =>sina=1/3 =>cosa=2√2/3 【∵在反三角函数里,如果反三角函数为正,θ∈[0,π]】 b=arccos1/4 =>cosb =1/4 =>sinb=√15/4 【后面推到的这个cosa=2√2/3和sinb=√15/4就是你自己画个三角形,根据比值而得的】 则sin(arcsin1/3 ...

π/3 sadasdaasdas

反函数高考不考的

① arcsin[cos(-7π/6)] =arcsin[cos(-π-π/6)] =arsin(-cosπ/6) =arcsin(-√3/2) =-π/3 ② 设α=arcsin3/5, β=arcsin8/17, α,β均是锐角 那么sinα=3/5,cosα=4/5 sinβ=8/17,cosβ=15/17 ∴sin(arcsin3/5+arcsin8/17) =sin(α+β) =sinαcosβ+cosαsinβ...

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