Numeric Response Numeric Response 4. If $\cos \theta=\frac{4}{7}$, the measure of $\theta$, to the nearest degree is (Record your answer in the numerical-response section below.) Your answer:

Step 1 ：Given that \(\cos \theta=\frac{4}{7}\).

Step 2 ：We can use the inverse cosine function, also known as arccos or cos^-1, to find the angle itself.

Step 3 ：First, convert the fraction to a decimal: \(\cos \theta = 0.5714285714285714\).

Step 4 ：Then, find the arccos of the decimal: \(\theta = \arccos(0.5714285714285714) = 0.9625507478846871\) radians.

Step 5 ：Convert the radians to degrees: \(\theta = 0.9625507478846871 \times \frac{180}{\pi} = 55.15009542095352\) degrees.

Step 6 ：Round the degrees to the nearest whole number: \(\theta = 55\) degrees.

Step 7 ：Final Answer: The measure of \(\theta\), to the nearest degree is \(\boxed{55}\).