Whakaoti mō j
j=\frac{-4k\sin(3t)-\frac{i\cos(t)}{t}}{5}
t\neq 0
Whakaoti mō k
\left\{\begin{matrix}k=-\frac{i\cos(t)+5jt}{4t\sin(3t)}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }t=\frac{\pi n_{1}}{3}\\k\in \mathrm{C}\text{, }&j=-\frac{i\cos(t)}{5t}\text{ and }t\neq 0\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }t=\frac{\pi n_{1}}{3}\end{matrix}\right.
Tohaina
Kua tāruatia ki te papatopenga
5tj+4\sin(3t)kt=-i\cos(t)
Tangohia te i\cos(t) mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.
5tj=-i\cos(t)-4\sin(3t)kt
Tangohia te 4\sin(3t)kt mai i ngā taha e rua.
5tj=-4kt\sin(3t)-i\cos(t)
He hanga arowhānui tō te whārite.
\frac{5tj}{5t}=\frac{-4kt\sin(3t)-i\cos(t)}{5t}
Whakawehea ngā taha e rua ki te 5t.
j=\frac{-4kt\sin(3t)-i\cos(t)}{5t}
Mā te whakawehe ki te 5t ka wetekia te whakareanga ki te 5t.
j=\frac{-4k\sin(3t)-\frac{i\cos(t)}{t}}{5}
Whakawehe -i\cos(t)-4kt\sin(3t) ki te 5t.
5tj+4\sin(3t)kt=-i\cos(t)
Tangohia te i\cos(t) mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.
4\sin(3t)kt=-i\cos(t)-5tj
Tangohia te 5tj mai i ngā taha e rua.
4t\sin(3t)k=-i\cos(t)-5jt
He hanga arowhānui tō te whārite.
\frac{4t\sin(3t)k}{4t\sin(3t)}=\frac{-i\cos(t)-5jt}{4t\sin(3t)}
Whakawehea ngā taha e rua ki te 4\sin(3t)t.
k=\frac{-i\cos(t)-5jt}{4t\sin(3t)}
Mā te whakawehe ki te 4\sin(3t)t ka wetekia te whakareanga ki te 4\sin(3t)t.
k=-\frac{\frac{i\cos(t)}{t}+5j}{4\sin(t)\left(4\left(\cos(t)\right)^{2}-1\right)}
Whakawehe -i\cos(t)-5tj ki te 4\sin(3t)t.
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