GIVEN:
The cosine of the angle is:
[tex]\cos \theta=\frac{4}{7}[/tex]
SOLUTION:
To find the measure of the angle, we can find the cos inverse of 4/7. Using a calculator:
[tex]\begin{gathered} \text{If }\cos \theta=\frac{4}{7}, \\ \text{then} \\ \theta=\cos ^{-1}(\frac{4}{7}) \\ \theta=55.15\degree \end{gathered}[/tex]
The problem gives that sin θ is negative and we can see that cos θ is positive. The image below shows which angles are positive and in which quadrant:
Therefore, the angle is in the 4th quadrant.
In the fourth quadrant, the value of the angle is:
[tex]\theta_1=360-\theta[/tex]
Therefore, the angle will be:
[tex]\begin{gathered} \theta_1=360-55.15 \\ \theta_1=304.85\degree \end{gathered}[/tex]
The angle is 304.85°
