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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