In Exercises 1–6, the measure of an angle is given. Classify the angle as acute, right, obtuse, or straight. 𝜋/2

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

Identify the given angle measure, which is \( \frac{\pi}{2} \) radians.

Compare the given angle \( \frac{\pi}{2} \) to the classifications: since it matches exactly \( \frac{\pi}{2} \), it fits the definition of a right angle.

Conclude that the angle \( \frac{\pi}{2} \) is classified as a right angle.

Remember that this classification is based on the radian measure and the standard angle definitions.

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주요 개념

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Radian Measure of Angles

Radian is a unit for measuring angles based on the radius of a circle. One radian is the angle subtended by an arc equal in length to the radius. Understanding radians allows conversion between radians and degrees, which is essential for classifying angles given in radian measure.

Classification of Angles

Angles are classified by their measure: acute angles are less than 90° (π/2 radians), right angles equal 90° (π/2 radians), obtuse angles are between 90° and 180° (π/2 to π radians), and straight angles equal 180° (π radians). This classification helps identify the type of angle from its measure.

Conversion Between Radians and Degrees

To classify angles given in radians, it is often helpful to convert them to degrees using the formula: degrees = radians × (180/π). This conversion aids in intuitive understanding and comparison with standard angle classifications.