1.5=1/cos(x) find x
$$\small{\text{$
\begin{array}{rcl}
\dfrac{ 1 } { \cos{(x)} } &=& 1.5 \\\\
\dfrac{ 1 } { \cos{(x)} } &=& \dfrac{3}{2} \\\\
\cos{(x)} &=& \dfrac{2}{3} \\\\
\cos{(x)} &=& \dfrac{2}{3} \qquad | \qquad \pm\arccos{()}\\\\
x &=& \pm \arccos{ \left(\dfrac{2}{3} \right) }\\\\
x_{1,2} &=& \pm 48.1896851042\ensurement{^{\circ}}\\\\
\mathbf{x_1} & \mathbf{=} & \mathbf{48.1896851042\ensurement{^{\circ}} } \\\\
x_2 &=& -48.1896851042\ensurement{^{\circ}} \\\\
x_2 &=& -48.1896851042\ensurement{^{\circ}} + 360 \ensurement{^{\circ}} \\\\
\mathbf{x_2} & \mathbf{=} & \mathbf{311.810314896\ensurement{^{\circ}} }
\end{array}
$}}$$
1.5=1/cos(x) find x
$$\small{\text{$
\begin{array}{rcl}
\dfrac{ 1 } { \cos{(x)} } &=& 1.5 \\\\
\dfrac{ 1 } { \cos{(x)} } &=& \dfrac{3}{2} \\\\
\cos{(x)} &=& \dfrac{2}{3} \\\\
\cos{(x)} &=& \dfrac{2}{3} \qquad | \qquad \pm\arccos{()}\\\\
x &=& \pm \arccos{ \left(\dfrac{2}{3} \right) }\\\\
x_{1,2} &=& \pm 48.1896851042\ensurement{^{\circ}}\\\\
\mathbf{x_1} & \mathbf{=} & \mathbf{48.1896851042\ensurement{^{\circ}} } \\\\
x_2 &=& -48.1896851042\ensurement{^{\circ}} \\\\
x_2 &=& -48.1896851042\ensurement{^{\circ}} + 360 \ensurement{^{\circ}} \\\\
\mathbf{x_2} & \mathbf{=} & \mathbf{311.810314896\ensurement{^{\circ}} }
\end{array}
$}}$$