Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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What is the double angle formula for sin(2θ)?

2sinθcosθ
sin²θ + cos²θ
sin(θ+θ)
tan(2θ)/2

The correct answer is: 2sinθcosθ

The double angle formula for sine is expressed as sin(2θ) = 2sinθcosθ. This formula is valuable because it provides a way to express the sine of a double angle in terms of the sine and cosine of the original angle θ. The significance of this formula lies in its applications throughout trigonometry, especially in solving equations and simplifying expressions that involve sine functions. For example, using this formula can convert complex expressions into simpler forms, making it easier to solve for unknowns or evaluate functions at specific angles. The other options do not represent the double angle formula correctly. The expression sin²θ + cos²θ is actually the Pythagorean identity, indicating that the square of sine plus the square of cosine of any angle equals one. The option sin(θ + θ) represents a sum angle identity, but does not detail how to simplify that into a specific formula. Finally, tan(2θ)/2 is not a standard representation related to the double angle for sine, and thus does not align with the established trigonometric identities.