In Exercises 55–58, use a calculator to find the value of the acute angle θ to the nearest degree. sin θ = 0.2974

Key Concepts

Inverse Trigonometric Functions

Inverse trigonometric functions, such as arcsin, arccos, and arctan, are used to find angles when the values of the trigonometric ratios are known. In this case, since sin θ = 0.2974, we can use the arcsin function to determine the angle θ. This function essentially reverses the sine operation, allowing us to solve for the angle corresponding to a given sine value.

Calculator Functions

Most scientific calculators have built-in functions for calculating inverse trigonometric values. To find θ when sin θ = 0.2974, you would input the value into the arcsin function on the calculator. It's important to ensure that the calculator is set to the correct mode (degrees or radians) based on the requirements of the problem, as this will affect the output angle.

Acute Angles

An acute angle is defined as an angle that measures less than 90 degrees. In the context of trigonometric functions, the sine function is positive in the first quadrant, where all angles are acute. Therefore, when solving for θ in this problem, we are specifically looking for the acute angle that corresponds to the sine value of 0.2974, ensuring that the solution falls within the appropriate range.