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. csc θ = 1.3861147

Key Concepts

Cosecant Function

The cosecant function, denoted as csc(θ), is the reciprocal of the sine function. It is defined as csc(θ) = 1/sin(θ). Understanding this relationship is crucial for solving equations involving csc, as it allows us to convert the cosecant expression into a sine expression, which can then be manipulated to find the angle θ.

Inverse Trigonometric Functions

Inverse trigonometric functions, such as arcsin, are used to find angles when given a trigonometric ratio. For example, if sin(θ) = x, then θ = arcsin(x). In this context, once we find sin(θ) from the given csc(θ), we can use the inverse sine function to determine the angle θ within the specified interval.

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 we need to ensure our final answer is expressed in this format. Understanding how to convert between radians and degrees, if necessary, is important for accurately reporting the angle θ.