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Questions and Answers
What is the formula for sin(A + B)?
What is the formula for sin(A + B)?
- sin A + sin B
- cos A + sin B
- sin A cos B + cos A sin B (correct)
- cos A cos B - sin A sin B
Which identity represents cos(A - B)?
Which identity represents cos(A - B)?
- cos A cos B + sin A sin B (correct)
- sin A sin B - cos A cos B
- cos A + cos B
- sin A cos B - cos A sin B
What is the result of sin 8 cos 8 in terms of a sine formula?
What is the result of sin 8 cos 8 in terms of a sine formula?
- 1/2 cos(2 * 8)
- 1/2 sin(2 * 8) (correct)
- sin 8 + cos 8
- sin(8 + 8)
How is cos(A + B) expressed in terms of sine and cosine?
How is cos(A + B) expressed in terms of sine and cosine?
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What is the relationship represented by cos 8 sin 9?
What is the relationship represented by cos 8 sin 9?
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Study Notes
Trigonometric Identities
- Sum of Angles for Sine: sin(A + B) = sin A cos B + cos A sin B
- Difference of Angles for Sine: sin(A - B) = sin A cos B - cos A sin B
- Sum of Angles for Cosine: cos(A + B) = cos A cos B - sin A sin B
- Difference of Angles for Cosine: cos(A - B) = cos A cos B + sin A sin B
Product-to-Sum Formulas
- Product of Sine and Cosine: sin(θ) cos(θ) = 1/2 sin(2θ)
- Product of Cosine with Itself: cos(θ) cos(θ) = 1/2 cos(2θ)
- Product of Sine and a Different Angle: cos(θ) sin(ϕ) = 1/2 sin(2(θ + ϕ))
General Observations
- These formulas are foundational in trigonometry, aiding in the simplification of expressions and solving equations.
- Understanding these transformations can enhance problem-solving skills in various mathematical contexts, including calculus and physics.
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