Find the Exact Value sin(55 degrees )

Problem

sin(55^∘)

Solution

1. Identify the expression as the sine of a non-standard angle, 55^∘

2. Determine if the angle can be expressed as a sum or difference of standard angles (e.g., 30^∘,45^∘,60^∘. Since 55^∘ is not a standard sum or difference of these angles, the exact value is typically represented in its trigonometric form.

3. Recognize that 55^∘ is the complement of 35^∘ so sin(55^∘)=cos(35^∘)

4. Conclude that without using complex radical nested forms (like those derived from 5^∘ increments), the simplest exact form is the expression itself.

Final Answer

sin(55^∘)=sin(55^∘)

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