Find a value of θ, in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. cot θ = 1.1249386
Table of contents
- 0. Review of College Algebra4h 45m
- 1. Measuring Angles40m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
1. Measuring Angles
Angles in Standard Position
Problem 4
Textbook Question
In Exercises 1–6, the measure of an angle is given. Classify the angle as acute, right, obtuse, or straight. 87.177°
Verified step by step guidance1
Recall the definitions of angle classifications: an acute angle is between 0° and 90°, a right angle is exactly 90°, an obtuse angle is between 90° and 180°, and a straight angle is exactly 180°.
Look at the given angle measure, which is 87.177°.
Compare 87.177° to the classification ranges: since 87.177° is greater than 0° but less than 90°, it falls within the acute angle range.
Conclude that the angle 87.177° is classified as an acute angle based on the comparison.
Remember that this classification helps in understanding the properties and relationships of angles in various geometric contexts.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Angle Measurement
Angle measurement is the process of determining the size of an angle in degrees. Degrees are a unit that divides a full rotation into 360 equal parts. Understanding how to read and interpret angle measures is fundamental to classifying angles correctly.
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Types of Angles
Angles are classified based on their degree measure: acute angles are less than 90°, right angles are exactly 90°, obtuse angles are greater than 90° but less than 180°, and straight angles are exactly 180°. Recognizing these categories helps in identifying the nature of any given angle.
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Comparison of Angle Measures
To classify an angle, compare its measure to the standard angle benchmarks (90° and 180°). This comparison allows you to determine whether the angle is acute, right, obtuse, or straight by placing it within the correct range of degrees.
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