Find the Exact Value csc(55)

Problem

csc(55^∘)

Solution

1. Identify the function and the angle. The task is to find the exact value of the cosecant of 55^∘

2. Relate the cosecant function to the sine function using the reciprocal identity.

csc(55^∘)=1/sin(55^∘)

3. Determine if the angle is a standard reference angle. The angle 55^∘ is not one of the standard angles (0^∘,30^∘,45^∘,60^∘,90^∘ found on the unit circle.

4. Evaluate the possibility of using sum or difference formulas. While 55^∘ can be written as 10^∘+45^∘ or 110^∘/2 these do not result in a standard radical form without involving nested radicals or higher-order roots from the triple-angle or quintuple-angle formulas.

5. Conclude that for most trigonometric contexts, the expression csc(55^∘) is already in its simplest exact form, or it can be expressed in terms of its cofunction.

csc(55^∘)=sec(35^∘)

Final Answer

csc(55^∘)=csc(55^∘)

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