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

Verified step by step guidance

1. Recognize that the expression \( \sin 35^\circ \cos 55^\circ + \cos 35^\circ \sin 55^\circ \) resembles the sine addition formula.
2. Recall the sine addition formula: \( \sin(A + B) = \sin A \cos B + \cos A \sin B \).
3. Identify \( A = 35^\circ \) and \( B = 55^\circ \) in the given expression.
4. Apply the sine addition formula: \( \sin(35^\circ + 55^\circ) \).
5. Calculate the angle sum: \( 35^\circ + 55^\circ = 90^\circ \), and use the fact that \( \sin 90^\circ = 1 \).

Key Concepts

Trigonometric Identities

Trigonometric identities are equations that involve trigonometric functions and are true for all values of the variables involved. A key identity relevant to this question is the sine addition formula, which states that sin(a + b) = sin(a)cos(b) + cos(a)sin(b). This identity allows us to simplify expressions involving sine and cosine of angles.

Sine and Cosine Functions

The sine and cosine functions are fundamental trigonometric functions that relate the angles of a right triangle to the ratios of its sides. For any angle θ, sin(θ) represents the ratio of the opposite side to the hypotenuse, while cos(θ) represents the ratio of the adjacent side to the hypotenuse. Understanding these functions is essential for evaluating trigonometric expressions.

Calculator Usage for Trigonometric Functions

Using a calculator to evaluate trigonometric functions involves inputting angles in degrees or radians to obtain the sine or cosine values. It is crucial to ensure that the calculator is set to the correct mode (degree or radian) based on the angle measurement. This allows for accurate computation of expressions involving trigonometric functions.