Solve {l}{tan(θ)=1}{a=sin(θ)}{b=a}{text{Solvefor}ctext{where}}{c=b}

$$\left. \begin{array} { l } { \tan(\theta) = 1 }\\ { a = \sin(\theta) }\\ { b = a }\\ { \text{Solve for } c \text{ where} } \\ { c = b } \end{array} \right.$$

Solve for θ, a, b, c (complex solution)

$$\theta =2\pi n_{1}+\frac{\pi }{4}\text{, }n_{1}\in \mathrm{Z}\text{, }a=\frac{\sqrt{2}}{2}\approx 0.707106781\text{, }b=\frac{\sqrt{2}}{2}\approx 0.707106781\text{, }c=\frac{\sqrt{2}}{2}\approx 0.707106781$$

$$\theta =2\pi n_{2}+\frac{5\pi }{4}\text{, }n_{2}\in \mathrm{Z}\text{, }a=-\frac{\sqrt{2}}{2}\approx -0.707106781\text{, }b=-\frac{\sqrt{2}}{2}\approx -0.707106781\text{, }c=-\frac{\sqrt{2}}{2}\approx -0.707106781$$

Solve for θ, a, b, c

$$\theta =2\pi n_{1}+\frac{5\pi }{4}\text{, }n_{1}\in \mathrm{Z}\text{, }a=-\frac{\sqrt{2}}{2}\approx -0.707106781\text{, }b=-\frac{\sqrt{2}}{2}\approx -0.707106781\text{, }c=-\frac{\sqrt{2}}{2}\approx -0.707106781$$

$$\theta =2\pi n_{2}+\frac{\pi }{4}\text{, }n_{2}\in \mathrm{Z}\text{, }a=\frac{\sqrt{2}}{2}\approx 0.707106781\text{, }b=\frac{\sqrt{2}}{2}\approx 0.707106781\text{, }c=\frac{\sqrt{2}}{2}\approx 0.707106781$$