COS(X)= -0.75. Estimate to the nearest hundredths if (X) is greater than or equal to 0* and less than 360*. ((*) = degrees)

COS(X)= -0.75.

Estimate to the nearest hundredths if (X) is greater than or equal to 0* and less than 360*. ((*) = degrees)

$0 \le x \le 360^{\circ}$

$\begin{array}{|rcll|} \hline \cos(x) &=& -0.75 \quad & | \quad \pm \arccos() \\ x &=& \pm \arccos(-0.75) \\ x &=& \pm 138.590377891^\circ \pm k \cdot 360^\circ\\ x_1 &=& 138.590377891^\circ \pm k \cdot 360^\circ \quad & k \in N \quad k= 0,1,2,3,\dots \\ \mathbf{x_1} &\mathbf{=}&\mathbf{ 138.590377891^\circ } \quad & 0 \le x \le 360^{\circ} \\\\ x_2 &=& -138.590377891^\circ \pm k \cdot 360^\circ \quad & k \in N \quad k= 0,1,2,3,\dots \\ x_2 &=& -138.590377891^\circ + 360^\circ \\ \mathbf{x_2} &\mathbf{=}&\mathbf{221.409622109^\circ } \quad & 0 \le x \le 360^{\circ} \\ \hline \end{array}$

COS(X)= -0.75

X =138.59 degrees.