Find a value of θ in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. See Example 2. sec θ = 1.1606249

Key Concepts

Secant Function

The secant function, denoted as sec(θ), is the reciprocal of the cosine function. It is defined as sec(θ) = 1/cos(θ). Understanding this relationship is crucial for solving equations involving secant, as it allows us to convert secant values into cosine values, which can then be used to find the angle θ.

Inverse Trigonometric Functions

Inverse trigonometric functions, such as arccosine (cos⁻¹), are used to find angles when given a trigonometric ratio. For example, if we have a cosine value, we can use the arccos function to determine the corresponding angle. This concept is essential for solving the equation sec(θ) = 1.1606249 by first converting it to cos(θ) and then applying the inverse function.

Angle Measurement in Degrees

In trigonometry, angles can be measured in degrees or radians. The problem specifies that the answer should be in decimal degrees, which means understanding how to convert between radians and degrees may be necessary. Additionally, knowing the range of angles (0° to 90°) helps in determining the correct quadrant for the solution.