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Question 11, 1.1.81 Points: 0 of 1 Find the angle of least positive measure (in degrees, not equal to the given measure) that is coterminal with A . The measure is \( \square \) \( ]^{\circ} \). (Simplify your answer.)

Ask by Gough Hardy. in the United States
Feb 03,2025

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Answer

To find the least positive coterminal angle with \( A \), subtract \( 360^\circ \) from \( A \) until the angle is between \( 0^\circ \) and \( 360^\circ \).

Solution

To find the angle of least positive measure that is coterminal with a given angle \( A \), we can use the following steps: 1. **Understanding Coterminal Angles**: Coterminal angles are angles that differ by a multiple of \( 360^\circ \). This means that if you have an angle \( A \), the coterminal angle can be found using the formula: \[ A + 360k \] where \( k \) is any integer. 2. **Finding the Least Positive Coterminal Angle**: To find the least positive coterminal angle, we can use the following steps: - If \( A \) is positive, subtract \( 360^\circ \) until the angle is less than \( 360^\circ \). - If \( A \) is negative, add \( 360^\circ \) until the angle is positive. 3. **Simplifying the Angle**: If the angle is already between \( 0^\circ \) and \( 360^\circ \), it is already in its simplest form. Now, let's denote the given angle \( A \) as \( x \). To proceed, please provide the value of \( A \) (or \( x \)) so that I can calculate the least positive coterminal angle.

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To find an angle that is coterminal with angle A, we need to add or subtract multiples of \( 360^\circ \) (since a full rotation is \( 360^\circ \)). For example, if you have an angle of \( 450^\circ \), you can subtract \( 360^\circ \) to find a coterminal angle: \[ 450^\circ - 360^\circ = 90^\circ. \] This means that \( 90^\circ \) is coterminal with \( 450^\circ \). If you happen to get a negative angle, simply add \( 360^\circ \) until the angle is positive! To provide a fresh example, if you start with \( -45^\circ \), adding \( 360^\circ \) gives you \( -45^\circ + 360^\circ = 315^\circ \), which is a positive angle coterminal with \( -45^\circ \). Just remember, the goal is always to arrive at a positive angle measure by either adding or subtracting \( 360^\circ \)!

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