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
2. Trigonometric Functions on Right Triangles
Trigonometric Functions on Right Triangles
2:39 minutes
Problem 65
Textbook Question
Textbook QuestionIn Exercises 63–68, find the exact value of each expression. Do not use a calculator. 1 + sin² 40° + sin² 50°
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Pythagorean Identity
The Pythagorean identity states that for any angle θ, sin²(θ) + cos²(θ) = 1. This fundamental relationship between sine and cosine is crucial for simplifying trigonometric expressions and solving equations. Understanding this identity allows students to manipulate and combine sine and cosine functions effectively.
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Pythagorean Identities
Sine Function Properties
The sine function is periodic and has specific values for common angles. Notably, sin(40°) and sin(50°) can be related through the complementary angle identity, where sin(θ) = cos(90° - θ). Recognizing these properties helps in evaluating expressions involving sine functions without a calculator.
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Graph of Sine and Cosine Function
Sum of Sine Squares
The expression sin²(θ) + sin²(φ) can often be simplified using trigonometric identities. In this case, knowing that sin²(θ) + sin²(φ) can be expressed in terms of cosines or combined using angle addition formulas is essential. This understanding aids in finding exact values for trigonometric expressions involving multiple angles.
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Sum and Difference of Sine & Cosine
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