In Exercises 1–6, the measure of an angle is given. Classify the angle as acute, right, obtuse, or straight. 𝜋
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
Radians
Problem 26
Textbook Question
Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). ―1800°
Verified step by step guidance1
Recall the formula to convert degrees to radians: \(\text{radians} = \text{degrees} \times \frac{\pi}{180}\).
Substitute the given degree measure into the formula: \(1800^\circ \times \frac{\pi}{180}\).
Simplify the fraction by dividing 1800 by 180: \(\frac{1800}{180} = 10\).
Express the result as a multiple of \(\pi\): \(10\pi\) radians.
Therefore, the degree measure \(1800^\circ\) is equivalent to \(10\pi\) radians.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Degree to Radian Conversion
Degrees and radians are two units for measuring angles. To convert degrees to radians, multiply the degree measure by π/180. This conversion is essential because radians are the standard unit in many mathematical contexts, especially calculus and trigonometry.
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Understanding Multiples of π
Expressing angles as multiples of π simplifies the representation of radian measures. Since π radians equal 180°, converting degrees to radians often results in fractions involving π, which should be left in this form for exactness and clarity.
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Simplifying Fractions
After converting degrees to radians, the resulting fraction should be simplified to its lowest terms. This makes the radian measure easier to interpret and use in further calculations, ensuring the answer is presented in the simplest exact form.
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