Use a calculator to determine whether each statement is true or false. A true statement may lead to results that differ in the last decimal place due to rounding error. 2 cos 38°22' = cos 76°44'
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 1
Textbook Question
In Exercises 1–6, the measure of an angle is given. Classify the angle as acute, right, obtuse, or straight. 135°
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 135°.
Compare 135° to the ranges defined: since 135° is greater than 90° but less than 180°, it falls into the obtuse angle category.
Therefore, classify the angle 135° as an obtuse angle based on the comparison.
Summarize: 135° is an obtuse angle because it lies between 90° and 180°.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Angle Measurement in Degrees
Angles are measured in degrees, representing the amount of rotation from one ray to another around a common vertex. A full circle is 360°, a straight angle is 180°, and smaller angles are fractions of this rotation.
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Classification of Angles
Angles are classified based on their 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°.
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Coterminal Angles
Comparing Angle Measures
To classify an angle, compare its degree measure to the standard angle categories. For example, 135° is greater than 90° but less than 180°, so it is classified as an obtuse angle.
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Reference Angles on the Unit Circle
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