Solution:
Given the equation:
[tex]\begin{gathered} \cos\theta=0.7361 \\ for\text{ 0}\leq\theta<360 \end{gathered}[/tex]
To find the values of θ, we take the inverse cosine of both sides,
Thus,
[tex]\begin{gathered} cos^{-1}(cos\theta)=cos^{-1}(0.7361) \\ \implies\theta=42.59975343 \end{gathered}[/tex]
The cosine of θ is also positive at the 4th quadrant.
Thus, at the 4th quadrant, the value of θ is
[tex]\begin{gathered} \theta^{\prime}=360-\theta \\ \implies\theta^{\prime}=360-42.59975343 \\ =317.4002466 \end{gathered}[/tex]
Hence, the values of θ, to 2 decimal places, for 0 °≤ θ < 360° are
[tex]\theta=42.60,\text{ 317.40 }[/tex]
