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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