SOLUTION
The given trigonometric equation is
[tex]\cos x=\frac{1}{5}[/tex]
Notice that the cos function is positive
Using the idea of the quadrant, notice that cosine is positive in the first and fourth quadrants.
The value of x in the first quadrant is:
[tex]\begin{gathered} x=\cos^{-1}(\frac{1}{5}) \\ x=78.5^{\circ} \end{gathered}[/tex]
Therefore the value of x in the first quadrant is 78.5 degrees.
The value of x in the fourth quadrant is
[tex]\begin{gathered} 360-x \\ =360-78.5 \\ =281.5 \end{gathered}[/tex]
Therefore the value of x in the fourth quadrant is 281.5 degrees.
