In Exercises 1–6, the measure of an angle is given. Classify the angle as acute, right, obtuse, or straight. 𝜋

검증된 단계별 안내

Understand the definitions of angle classifications in radians: an acute angle is between 0 and \( \frac{\pi}{2} \), a right angle is exactly \( \frac{\pi}{2} \), an obtuse angle is between \( \frac{\pi}{2} \) and \( \pi \), and a straight angle is exactly \( \pi \).

Identify the given angle measure, which is \( \pi \) radians in this problem.

Compare the given angle \( \pi \) to the classification ranges: since it matches exactly \( \pi \), it fits the definition of a straight angle.

Conclude that the angle \( \pi \) radians is classified as a straight angle.

Remember that these classifications help in understanding the size and properties of angles in trigonometry and geometry.

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주요 개념

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Radian Measure of Angles

Angles can be measured in radians, where 𝜋 radians equal 180 degrees. Understanding radian measure is essential to classify angles given in radians by converting or comparing them to known angle measures.

Classification of Angles

Angles are classified based on their measure: acute (less than 90° or 𝜋/2 radians), right (exactly 90° or 𝜋/2 radians), obtuse (between 90° and 180° or between 𝜋/2 and 𝜋 radians), and straight (exactly 180° or 𝜋 radians).

Conversion Between Degrees and Radians

To classify angles given in radians, it is often helpful to convert between degrees and radians using the relationship 180° = 𝜋 radians. This aids in understanding and comparing angle sizes intuitively.