r(t)=cos(t)i+5tj+4sin(3t)kquadt=0 eching

$$r ( t ) = \cos ( t ) i + 5 t j + 4 \sin ( 3 t ) k \quad t = 0$$

j uchun yechish

$$j=\frac{-4k\sin(3t)-\frac{i\cos(t)}{t}}{5}$$

$$t\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan i\cos(t) ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$5tj+4\sin(3t)kt=-i\cos(t)$$

Ikkala tarafdan 4\sin(3t)kt ni ayirish.

$$5tj=-i\cos(t)-4\sin(3t)kt$$

Tenglama standart shaklda.

$$5tj=-4kt\sin(3t)-i\cos(t)$$

Ikki tarafini 5t ga bo‘ling.

$$\frac{5tj}{5t}=\frac{-4kt\sin(3t)-i\cos(t)}{5t}$$

5t ga bo'lish 5t ga ko'paytirishni bekor qiladi.

$$j=\frac{-4kt\sin(3t)-i\cos(t)}{5t}$$

-i\cos(t)-4kt\sin(3t) ni 5t ga bo'lish.

$$j=\frac{-4k\sin(3t)-\frac{i\cos(t)}{t}}{5}$$

k uchun yechish

$$\left\{\begin{matrix}k=-\frac{i\cos(t)+5jt}{4t\sin(3t)}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }t=\frac{\pi n_{1}}{3}\\k\in \mathrm{C}\text{, }&j=-\frac{i\cos(t)}{5t}\text{ and }t\neq 0\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }t=\frac{\pi n_{1}}{3}\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan i\cos(t) ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$5tj+4\sin(3t)kt=-i\cos(t)$$

Ikkala tarafdan 5tj ni ayirish.

$$4\sin(3t)kt=-i\cos(t)-5tj$$

Tenglama standart shaklda.

$$4t\sin(3t)k=-i\cos(t)-5jt$$

Ikki tarafini 4\sin(3t)t ga bo‘ling.

$$\frac{4t\sin(3t)k}{4t\sin(3t)}=\frac{-i\cos(t)-5jt}{4t\sin(3t)}$$

4\sin(3t)t ga bo'lish 4\sin(3t)t ga ko'paytirishni bekor qiladi.

$$k=\frac{-i\cos(t)-5jt}{4t\sin(3t)}$$

-i\cos(t)-5tj ni 4\sin(3t)t ga bo'lish.

$$k=-\frac{\frac{i\cos(t)}{t}+5j}{4\sin(t)\left(4\left(\cos(t)\right)^{2}-1\right)}$$