Solve {l}{cos(A)=1/2}{sin(B)=1/sqrt{2}}{a={(pi)}}{text{Solvefor}btext{where}}{b=a}

$$\left. \begin{array} { l } { \cos(A) = \frac{1}{2} }\\ { \sin(B) = \frac{1}{\sqrt{2}} }\\ { a = {(\pi)} }\\ { \text{Solve for } b \text{ where} } \\ { b = a } \end{array} \right.$$

Solve for A, B, a, b

$$A=2\pi n_{1}+\frac{\pi }{3}\text{, }n_{1}\in \mathrm{Z}\text{, }B=2\pi n_{3}+\frac{\pi }{4}\text{, }n_{3}\in \mathrm{Z}\text{, }a=\pi \approx 3.141592654\text{, }b=\pi \approx 3.141592654$$

$$A=2\pi n_{1}+\frac{\pi }{3}\text{, }n_{1}\in \mathrm{Z}\text{, }B=2\pi n_{4}+\frac{3\pi }{4}\text{, }n_{4}\in \mathrm{Z}\text{, }a=\pi \approx 3.141592654\text{, }b=\pi \approx 3.141592654$$

$$A=2\pi n_{2}+\frac{5\pi }{3}\text{, }n_{2}\in \mathrm{Z}\text{, }B=2\pi n_{3}+\frac{\pi }{4}\text{, }n_{3}\in \mathrm{Z}\text{, }a=\pi \approx 3.141592654\text{, }b=\pi \approx 3.141592654$$

$$A=2\pi n_{2}+\frac{5\pi }{3}\text{, }n_{2}\in \mathrm{Z}\text{, }B=2\pi n_{4}+\frac{3\pi }{4}\text{, }n_{4}\in \mathrm{Z}\text{, }a=\pi \approx 3.141592654\text{, }b=\pi \approx 3.141592654$$