แก้โจทย์ {l}{sin(θ)=cos(θ)}{a=θ}{b=a}{text{Solvefor}ctext{where}}{c=b}

$$\left. \begin{array} { l } { \sin(\theta) = \cos(\theta) }\\ { a = \theta }\\ { b = a }\\ { \text{Solve for } c \text{ where} } \\ { c = b } \end{array} \right.$$

หาค่า θ, a, b, c (complex solution)

$$\theta =\pi n_{1}+\frac{\pi }{4}$$

$$n_{1}\in \mathrm{Z}$$

$$a=\pi n_{1}+\frac{\pi }{4}$$

$$n_{1}\in \mathrm{Z}$$

$$b\in \cup n_{1},\pi n_{1}+\frac{\pi }{4}$$

$$n_{1}\in \mathrm{Z}$$

$$c\in \cup n_{1},\cup n_{1},\cup n_{1},\cup n_{1},\pi n_{1}+\frac{\pi }{4}$$

$$b=\pi n_{1}+\frac{\pi }{4}$$

$$n_{1}\in \mathrm{Z}$$

หาค่า θ, a, b, c

$$\theta =2\pi n_{1}+\frac{5\pi }{4}\text{, }n_{1}\in \mathrm{Z}\text{, }a=2\pi n_{1}+\frac{5\pi }{4}\text{, }n_{1}\in \mathrm{Z}\text{, }b=2\pi n_{1}+\frac{5\pi }{4}\text{, }n_{1}\in \mathrm{Z}\text{, }c=2\pi n_{1}+\frac{5\pi }{4}\text{, }n_{1}\in \mathrm{Z}$$

$$\theta =2\pi n_{2}+\frac{\pi }{4}\text{, }n_{2}\in \mathrm{Z}\text{, }a=2\pi n_{2}+\frac{\pi }{4}\text{, }n_{2}\in \mathrm{Z}\text{, }b=2\pi n_{2}+\frac{\pi }{4}\text{, }n_{2}\in \mathrm{Z}\text{, }c=2\pi n_{2}+\frac{\pi }{4}\text{, }n_{2}\in \mathrm{Z}$$