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