Multiple Choice
Convert the angle radians to degrees, rounding to the nearest tenth.
75
views
1. Measuring Angles
Radians
1:12 minutesProblem 5
Textbook Question
In Exercises 1–6, the measure of an angle is given. Classify the angle as acute, right, obtuse, or straight. 𝜋
Verified step by step guidance1
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.
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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.
Recommended video:
5:04
Converting between Degrees & Radians
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).
Recommended video:
04:46Coterminal Angles
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.
Recommended video:
5:04Converting between Degrees & Radians
Related Videos
Related Practice