sinht和cosht公式

殷米岚1068求双曲螺旋线 r={acosht,asinht,at}从t=0起计算的弧长 -
耿伟趴19381233475 ______ 求双曲螺旋线 r={acosht,asinht,at}从t=0起到t=T的弧长I(T). I(T)=∫{0→T}√[(acosht)'^2+(asinht)'^2+(at)'^2]dt= =a∫{0→T}√[(sinht)^2+(cosht)^2+1]dt= =a∫{0→T}√[2(cosht)^2]dt= =a√2∫{0→T}coshtdt=a√2sinhT.

殷米岚1068求双曲螺旋线 r={acosht,asinht,at}从t=0起计算的弧长 -
耿伟趴19381233475 ______[答案] 求双曲螺旋线 r={acosht,asinht,at}从t=0起到t=T的弧长I(T). I(T)=∫{0→T}√[(acosht)'^2+(asinht)'^2+(at)'^2]dt= =a∫{0→T}√[(sinht)^2+(cosht)^2+1]dt= =a∫{0→T}√[2(cosht)^2]dt= =a√2∫{0→T}coshtdt=a√2sinhT.

殷米岚1068arcosh5x=arsinh4x x=?
耿伟趴19381233475 ______ 令t=arccosh5x 则x=cosht/5=sinht/4 得tanht=4/5=m 于是sinh2t=40/9 (万能公式 sinh2x=2m/(1-m^2)) 而sinht=4x cosht=5x sinh2t=2sinhtcosht=40x^2 于是x=土1/3

殷米岚1068r(t)=(cosht,sinht,t).–1≤t≤1.求弧长 -
耿伟趴19381233475 ______ 一般的,双曲线(希腊语“ὑπερβολή”,字面意思是“超过”或“超出”)是定义为平面交截直角圆锥面的两半的一类圆锥曲线. 它还可以定义为与两个固定的点(叫做焦点)的距离差是常数的点的轨迹.这个固定的距离差是a的两倍,这里...

殷米岚1068数学求双曲螺旋线r={acosht,asinht,at}从t=0
耿伟趴19381233475 ______ 求双曲螺旋线 r={acosht,asinht,at}从t=0起到t=T的弧长I(T). I(T)=∫{0→T}√[(acosht)'^2+(asinht)'^2+(at)'^2]dt= =a∫{0→T}√[(sinht)^2+(cosht)^2+1]dt= =a∫{0→T}√[2(cosht)^2]dt= =a√2∫{0→T}coshtdt=a√2sinhT.

殷米岚1068arcosh5x=arsinh4x x=?会答的加分~要过程 -
耿伟趴19381233475 ______[答案] 令t=arccosh5x 则x=cosht/5=sinht/4 得tanht=4/5=m 于是sinh2t=40/9 (万能公式 sinh2x=2m/(1-m^2)) 而sinht=4x cosht=5x sinh2t=2sinhtcosht=40x^2 于是x=土1/3

殷米岚1068如果X=sinht 那么t=?x -
耿伟趴19381233475 ______ t=arsinhx