Use a calculator to evaluate each expression. sin 35° cos 55° + cos 35° sin 55°

검증된 단계별 안내

Recognize that the expression \( \sin 35^\circ \cos 55^\circ + \cos 35^\circ \sin 55^\circ \) matches the sine addition formula, which is \( \sin A \cos B + \cos A \sin B = \sin (A + B) \).

Identify the angles \( A = 35^\circ \) and \( B = 55^\circ \) in the expression.

Rewrite the expression using the sine addition formula as \( \sin (35^\circ + 55^\circ) \).

Simplify the angle inside the sine function: \( 35^\circ + 55^\circ = 90^\circ \). So the expression becomes \( \sin 90^\circ \).

Use a calculator or recall that \( \sin 90^\circ = 1 \) to evaluate the expression.

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주요 개념

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Sine and Cosine Functions

Sine and cosine are fundamental trigonometric functions that relate the angles of a right triangle to the ratios of its sides. They are periodic and defined for all real numbers, often used to model oscillatory behavior. Understanding their values at specific angles is essential for evaluating expressions.

Angle Sum Identity for Sine

The angle sum identity states that sin(A + B) = sin A cos B + cos A sin B. This formula allows the expression sin 35° cos 55° + cos 35° sin 55° to be simplified directly to sin(35° + 55°), making calculations easier and more intuitive.

Using a Calculator for Trigonometric Values

Calculators can compute sine and cosine values for given angles, typically in degrees or radians. Ensuring the calculator is set to the correct mode (degrees here) is crucial for accurate results. This skill helps in evaluating trigonometric expressions numerically.