Table of contents
- 0. Review of College Algebra4h 43m
- 1. Measuring Angles39m
- 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
Complementary and Supplementary Angles
Problem 70
Textbook Question
Textbook QuestionSolar Eclipse on Neptune (Refer to Exercise 69.) The sun's distance from Neptune is approximately 2,800,000,000 mi (2.8 billion mi). The largest moon of Neptune is Triton, with a diameter of approximately 1680 mi. (Data from The World Almanac and Book of Facts.) b. Triton is approximately 220,000 mi from Neptune. Is it possible for Triton to cause a total eclipse on Neptune?
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Angular Size
Angular size refers to how large an object appears to an observer from a given distance. It is determined by the object's actual size and its distance from the observer. In the context of eclipses, the angular size of the moon (Triton) relative to the sun is crucial in determining whether it can completely cover the sun when viewed from Neptune.
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Example 2
Eclipse Geometry
Eclipse geometry involves the spatial arrangement of the sun, moon, and planet during an eclipse. For a total eclipse to occur, the moon must be directly between the sun and the planet, with the moon's angular size being equal to or greater than that of the sun as seen from the planet. Understanding this geometry helps in assessing the conditions under which Triton could cause a total eclipse on Neptune.
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Adding Vectors Geometrically
Distance and Scale
Distance and scale are fundamental in understanding celestial events. The vast distances between celestial bodies, such as the sun, Neptune, and Triton, affect their apparent sizes and the likelihood of eclipses. In this scenario, calculating the distances involved helps determine if Triton is sufficiently large and close enough to Neptune to block the sun's light entirely.
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Example 2
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