Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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What is the formula for sin(α ± β)?

sinαsinβ ± cosαcosβ
sinαcosβ ± cosαsinβ
cosαsinβ ± sinαcosβ
sinα + sinβ

The correct answer is: sinαcosβ ± cosαsinβ

The formula for sine of the sum or difference of two angles is a foundational concept in trigonometry. The correct expression for the sine of the sum or difference is: sin(α + β) = sinαcosβ + cosαsinβ sin(α - β) = sinαcosβ - cosαsinβ This relationship shows how the sine of the sum or difference of two angles can be expressed in terms of the sine and cosine of the individual angles. This is crucial because it allows for simplifications in many mathematical problems involving trigonometric functions. The first part, sinαcosβ, represents the sine of the first angle multiplied by the cosine of the second, while the second term (cosαsinβ) captures the sine of the second angle multiplied by the cosine of the first. This relationship is particularly useful in various applications such as solving triangles, analyzing wave patterns, and in calculus for integration and differentiation of trigonometric functions. The other choices do not represent the correct formula and do not capture the appropriate relationships between sine and cosine as clearly as option B does.