Questions: Use a calculator to find the value of the following expression rounded to two decimal places. cos^(-1)(11/13) / cos^(-1)(11/13) = square radian(s) (Type your answer in radians. Round to the nearest hundredth as needed.)

Use a calculator to find the value of the following expression rounded to two decimal places.

cos^(-1)(11/13) / cos^(-1)(11/13) = square radian(s)

(Type your answer in radians. Round to the nearest hundredth as needed.)

Transcript text: Use a calculator to find the value of the following expression rounded to two decimal places. \[ \frac{\cos ^{-1} \frac{11}{13}}{\cos ^{-1} \frac{11}{13}=\square \text { radian(s) }} \] (Type your answer in radians. Round to the nearest hundredth as needed.)

Solution

Solution Steps

To solve this problem, we need to calculate the inverse cosine (arccos) of the fraction \( \frac{11}{13} \) and then round the result to two decimal places. This involves using a calculator or a programming language like Python to compute the arccosine and format the output.

Step 1: Calculate the Inverse Cosine

To find the value of \( \cos^{-1} \left( \frac{11}{13} \right) \), we use the inverse cosine function. The result is approximately \( 0.5621 \) radians.

Step 2: Round the Result

Round the result from Step 1 to two decimal places. This gives us \( 0.56 \).