Answer to Question #151160 in Trigonometry for cherrina

Question

sin V = 0.2588

Answer 1

$\textsf{If }sin\theta=\alpha,\\\textsf{The general solution of the equation }sinV=\alpha\textsf{ is}\\ V=n180°+(-1)^n\theta\\ \textsf{where n is an integer (positive, negative, or zero)}\\ sin V=0.2588\\ \textsf{From tables, } sin15\degree=0.2588, \textsf{hence }V=15°\textsf{is a solution}\\ \textsf{Thus, the general solution is}\\ V=n180°+(-1)^n15°\\ \textsf{When n= 0 or 1 we obtain the solutions in the range 0° to 360°}\\ \textsf{When }n=0, V=15°\\ \textsf{When }n=1, V=165°\\$