Question

solve y=sin(x+c) for c with 2 given values for x and y

Answer 1

Conditions

solve $y = \sin(x + c)$ for $c$ with 2 given values for $x$ and $y$

Solution

$$\begin{array}{l} y = \sin(x + c) \\ x + c = \arcsin(y) + 2\pi n, \, n \in \mathbb{Z}; \, c = \arcsin(y) - x + 2\pi n \end{array}$$

For example, let's $x = 0$, $y = 0$. Then

$$0 = \sin(0 + c), \sin c = 0, \, c = \pi n, \, n \in \mathbb{Z}$$