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
6. Trigonometric Identities and More Equations
Sum and Difference Identities
Problem 5.30a
Textbook Question
Textbook QuestionWrite each function value in terms of the cofunction of a complementary angle.
sin 98.0142°
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Cofunction Identities
Cofunction identities in trigonometry relate the values of trigonometric functions of complementary angles. For example, the sine of an angle is equal to the cosine of its complement: sin(θ) = cos(90° - θ). This relationship is crucial for rewriting trigonometric functions in terms of their cofunctions, especially when dealing with angles that sum to 90 degrees.
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Cofunction Identities
Complementary Angles
Complementary angles are two angles whose measures add up to 90 degrees. In the context of trigonometric functions, if one angle is known, the other can be easily determined. Understanding complementary angles is essential for applying cofunction identities effectively, as it allows for the transformation of functions based on their angle relationships.
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Angle Measurement
Angle measurement can be expressed in degrees or radians, with degrees being the more common unit in basic trigonometry. In this question, the angle 98.0142° exceeds 90 degrees, indicating that it is not directly complementary to another angle. Recognizing how to convert or relate angles greater than 90 degrees to their complementary counterparts is important for applying trigonometric identities correctly.
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