Use a calculator to approximate each real number value. (Be sure the calculator is in radian mode.) 
y = cos⁻¹ (―0.32647891)

Verified step by step guidance

1. Ensure your calculator is in radian mode. This is crucial because the problem specifies that the calculation should be done in radians.
2. Identify the function you need to use: \( y = \cos^{-1}(-0.32647891) \). This is the inverse cosine function, which will give you the angle whose cosine is \(-0.32647891\).
3. Enter the value \(-0.32647891\) into your calculator using the inverse cosine function. This is often labeled as \( \cos^{-1} \) or \( \text{acos} \) on calculators.
4. The calculator will output an angle in radians. This is the value of \( y \).
5. Interpret the result: The range of the inverse cosine function is from 0 to \( \pi \) radians, so the result will be within this interval.

Key Concepts

Inverse Trigonometric Functions

Inverse trigonometric functions, such as cos⁻¹ (arccosine), are used to find the angle whose cosine is a given value. These functions are essential for solving problems where the angle is unknown, and they return values within specific ranges, typically between 0 and π for arccosine.

Radian Measure

Radian measure is a way of measuring angles based on the radius of a circle. One radian is the angle formed when the arc length is equal to the radius. Understanding radian measure is crucial when using calculators, as many trigonometric functions are often computed in radians rather than degrees.

Calculator Settings

Using a calculator in the correct mode (radian or degree) is vital for accurate trigonometric calculations. When solving problems involving inverse trigonometric functions, ensuring the calculator is set to radian mode will yield the correct angle in radians, which is necessary for further calculations or applications.