sintcost等于什么

费鹏天2515x=acos^3t,y=asin^3t,求dy/dx -
奚纨伊17288795024 ______ 显然 dx/dt =d (acos^3t) /dt =3acos²t * (cost)'= -3a*sint *cos²t 而dy/dt =d(asin^3t) /dt =3asin²t * (sint)'= 3a*sin²t *cost 所以 dy/dx = (dy/dt) / (dx/dt) = (3a*sin²t *cost) / (-3a*sint *cos²t) = -tant

费鹏天2515(sint+cost)/(cost - sint)怎么算的,等于tan(t+π/4) -
奚纨伊17288795024 ______[答案] (sint + cost) / (cost-sint) = [(sint + cost)/√2] / [(cost - sint)/√2] = (sint cosπ/4 + cost sinπ/4) / (cost cosπ/4 - sint sinπ/4) = sin(t+π/4) / cos(t+π/4) = tan(t+π/4)

费鹏天2515y=根号(3)x - 3根号(3) 转化为参数方程.是带sint和cost的那种.高分求! -
奚纨伊17288795024 ______ y=√3x-3√3 √3x-y=3√3 x/3-y/(3√3)=1 根据公式:cos2t=2cos²t-1 即2cos²t-cos2t=1 则可令:x/3=2cos²t,y/(3√3)=cos2t 即参数方程为: x=6cos²t, y=3√3cos2t

费鹏天2515x=sintcost y=sinx/cosx求导 -
奚纨伊17288795024 ______[答案] y = sinx/cosx dy/dx = [(sinx)' cosx - sinx (cosx)'] / cos²x = (cos²x + sin²x) / cos²x = 1/cos²x x = sint cost dx/dt = (sint)' cost + sint (cost)' = cos²t - sin²t dy/dt = (dy/dx)(dx/dt) = (1/cos²x)(cos²t - sin²t) = (cos²t - sin²t) / cos²(sint cost) 如果题目是...

费鹏天2515如何证明sint,sin2t,sinnt线性无关 -
奚纨伊17288795024 ______ sin(nt)可以展开成f(sint,cost)的形式. 并且f是关于sint,cost的二元n次多项式. 就是说你给的函数组中的每一项,是一个关于sint,cost次数递增的二元多项式. 而高次多项式,不能被低次多项式线性表示. 所以上述函数组线性无关.

费鹏天2515求证cos α/(1+sin α) - sinα/(1+cos α)=2(cos α - sin α)/(1+sin α+cos α) -
奚纨伊17288795024 ______ 证明:令α=2t; 等式左边= cos α/(1+sin α) -sinα/(1+cos α)=cos2t/(1+sin2t)-sin2t/(1+cos2t)=(cos²t-sin²t)/(cos²t+sin²t+2sint*cost)-2sint*cost/2cos²t -----降倍升幂=(cost-sint)/(cost+sint)-sint/cost -----化简、通分=(cos²t-sin²t-2sintcost)/cost(cost+sint) -----升倍降幂=(cos2t-sin2t)/[1/2(cos2t+1)+1/2sin2t]=2(cosα-sinα)/(1+sinα+cosα)=等式右边 证毕.

费鹏天2515多少的导数是sint+sintcost -
奚纨伊17288795024 ______ 根据题意有:y'=sint+sintcost y'=sint(1+cost)=sint[1+2cos^2(t/2)-1]=2cos^2(t/2)*2sin(t/2)cos(t/2)=4cos^3(t/2)sin(t/2) 两边积分得到:∫y'dt=4∫cos^3(t/2)sin(t/2)dt=8∫cos^3(t/2)sin(t/2)d(t/2)=-8∫cos^3(t/2)dcos(t/2) ∫y'dt=-2∫d[cos(t/2)]^4 所以:y=-2[cos(t/2)]^4+c.

费鹏天2515x=sint+cost y=sintcost 化为普通方程. -
奚纨伊17288795024 ______ ∵(sint+cost)²=sin²t+2sintcost+cos²t=1+2sintcost ∴x²=1+2y ∴y=x²/2-1/2

费鹏天2515参数方程x=cost+sint,y=sint*cost*(t为参数)的普通方程是多少 -
奚纨伊17288795024 ______[答案] 需要注意的是有个隐藏条件:(sint)^2+(cost)^2=1 即 (sint+cost)^2-2sint*cost=1 将x=cost+sint,y=sint*cost 代入得 x^2-2y=1,即 y=(x^2)/2-1/2

费鹏天2515x=tant,求dx -
奚纨伊17288795024 ______[答案] dx=dtant=d(sint/cost) =[(sint)'cost-sint(cost)']/(cost)^2 dt =[cost*cost+sint*sint]/(cost)^2 dt =1/(cost)^2 dt