In Exercises 35–60, find the reference angle for each angle. 5.5

Verified step by step guidance

1. Identify the given angle, which is 5.5 radians in this problem.
2. Recall that the reference angle is the acute angle formed between the terminal side of the given angle and the x-axis.
3. Since 5.5 radians is between \(\pi\) and \(2\pi\) (approximately 3.1416 and 6.2832), the angle lies in the fourth quadrant.
4. To find the reference angle \(\theta_{ref}\) in the fourth quadrant, use the formula: \(\theta_{ref} = 2\pi - \theta\), where \(\theta\) is the given angle.
5. Substitute the given angle into the formula: \(\theta_{ref} = 2\pi - 5.5\), and simplify to find the reference angle.

Key Concepts

Reference Angle

A reference angle is the acute angle formed between the terminal side of a given angle and the x-axis. It is always positive and less than or equal to 90°, used to simplify trigonometric calculations by relating any angle to an acute angle.

Standard Position of an Angle

An angle is in standard position when its vertex is at the origin and its initial side lies along the positive x-axis. Understanding this helps in determining the quadrant in which the terminal side lies, which is essential for finding the correct reference angle.

Quadrants and Angle Measurement

The coordinate plane is divided into four quadrants, each affecting the sign and calculation of angles. Knowing the quadrant of the terminal side helps determine how to calculate the reference angle by subtracting or adding the angle from 180°, 360°, or 0°.