Here are the essential concepts you must grasp in order to answer the question correctly.
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). This means that to find the angle θ when given csc(θ), one must first determine sin(θ) by taking the reciprocal of the given value. Understanding this relationship is crucial for solving problems involving cosecant.
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Inverse Trigonometric Functions
Inverse trigonometric functions, such as arcsin, are used to find angles when the value of a trigonometric function is known. For example, if sin(θ) is known, θ can be found using θ = arcsin(value). In this case, after calculating sin(θ) from csc(θ), the angle can be determined using the inverse sine function, ensuring the angle lies within the specified interval.
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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. The interval [0°, 90°) indicates that the solution must be a positive acute angle, reinforcing the need to ensure the calculated angle falls within this range.
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