Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is in the correct mode.)
sec 11𝜋/8


To evaluate \( \sec\left(\frac{11\pi}{8}\right) \), we follow these steps:

1. Recognize that \( \sec \theta = \frac{1}{\cos \theta} \). So we need to compute \( \cos\left(\frac{11\pi}{8}\right) \) first.
   
2. Ensure that the calculator is in **radian mode** since the angle is in terms of \( \pi \).

3. Compute \( \cos\left(\frac{11\pi}{8}\right) \).

4. Take the reciprocal of that value to find \( \sec\left(\frac{11\pi}{8}\right) \).

Now, let's calculate it:

\[
\sec\left(\frac{11\pi}{8}\right) = \frac{1}{\cos\left(\frac{11\pi}{8}\right)}
\]

Using a calculator:

\[
\cos\left(\frac{11\pi}{8}\right) \approx -0.3827
\]

\[
\sec\left(\frac{11\pi}{8}\right) = \frac{1}{-0.3827} \approx -2.6131
\]

So, the value of \( \sec\left(\frac{11\pi}{8}\right) \) is approximately **-2.6131**.

Would you like further clarification or details?

Here are 5 related questions for further exploration:

1. What is the sine of \( \frac{11\pi}{8} \)?
2. How would you evaluate \( \csc\left(\frac{11\pi}{8}\right) \)?
3. Can you explain the difference between degrees and radians in trigonometry?
4. What is the secant of \( \frac{5\pi}{4} \), and how does it compare to \( \frac{11\pi}{8} \)?
5. How do you determine the quadrant in which \( \frac{11\pi}{8} \) lies?

**Tip**: Always double-check that your calculator is in the correct mode (radians or degrees) when working with trigonometric functions to avoid incorrect results!

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is in the correct mode.) sec 11𝜋/8

Learn how to evaluate sec(11π/8) using a calculator in radian mode. This detailed solution includes the steps to find the cosine of 11π/8 and its reciprocal, sec(11π/8), rounded to four decimal places. Suitable for high school students in Grades 9-12.

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