The expression you're asking about is \(\cos^{-1} \left(\frac{3}{4}\right)\), which represents the inverse cosine (or arccosine) of \(\frac{3}{4}\). 

The arccosine function returns the angle \(\theta\) whose cosine is \(\frac{3}{4}\). This angle will be in the range \([0, \pi]\) (or \(0^\circ\) to \(180^\circ\)).

To calculate this:

\[
\theta = \cos^{-1} \left(\frac{3}{4}\right)
\]

Using a calculator:

\[
\theta \approx 0.7227 \, \text{radians}
\]

In degrees, this is approximately:

\[
\theta \approx 41.41^\circ
\]

Would you like more details or have any other questions?

### Related Questions:
1. What is the relationship between arccosine and cosine?
2. How would you find \(\cos^{-1}(-\frac{3}{4})\)?
3. What is the geometric interpretation of inverse trigonometric functions?
4. Can you derive the formula for \(\cos^{-1}(x)\) using a right triangle?
5. How can we use inverse trigonometric functions in solving real-world problems?

**Tip:** When working with inverse trigonometric functions, always ensure the input value lies within the valid domain, and check whether you want the result in degrees or radians.

Learn how to calculate the inverse cosine of 3/4 and convert the result to degrees. This trigonometry problem explains the use of the inverse cosine function and provides the solution in both radians (0.7227) and degrees (41.41°). Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation