Find the Exact Value csc(65)

Problem

csc(65)

Solution

1. Identify the function and the angle. The task is to find the exact value of the cosecant of 65

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

csc(65)=1/sin(65)

3. Express the angle 65 as a sum or difference of standard angles if possible. Since 65 is not a standard angle (like 30,45,60 or a simple combination of them that results in a standard radical form, the exact value is typically represented in terms of sine or cosine.

4. Determine if a radical form exists. While 65 can be written as 45+20 or 90−25 these do not lead to a standard algebraic constant involving simple square roots.

5. Conclude that without further context or specific identities for 5 increments, the exact value is the reciprocal of the sine of the angle.

Final Answer

csc(65)=1/sin(65)

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