Find the Exact Value csc(25)

Problem

csc(25)

Solution

1. Identify the expression as the cosecant of an angle measured in degrees.

2. Apply the reciprocal identity for cosecant, which states that csc(θ)=1/sin(θ)

3. Substitute the given angle into the identity.

csc(25)=1/sin(25)

4. Determine if the angle 25 is a standard reference angle (like 30 45 or 60. Since 25 is not a standard angle, its exact value cannot be expressed using simple radicals or integers without using complex trigonometric formulas (like those for 5.

5. Conclude that the simplest exact form is the reciprocal of the sine function.

Final Answer

csc(25)=1/sin(25)

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