Find the Exact Value sin(28 degrees )

Problem

sin(28^∘)

Solution

1. Identify the task as finding the exact trigonometric value of sin(28^∘)

2. Determine if the angle 28^∘ is a standard angle (like 0^∘,30^∘,45^∘,60^∘,90^∘ or a multiple of standard angles that can be expressed using sum, difference, or half-angle formulas.

3. Analyze the angle 28^∘ It is not a standard angle, nor is it easily expressed as a simple combination of standard angles (e.g., 15^∘=45^∘−30^∘ or 75^∘=45^∘+30^∘.

4. Conclude that while sin(28^∘) can be expressed in terms of radicals using complex algebraic methods (such as the triple-angle formula for 84^∘ or 14^∘, it does not have a simplified "exact value" form commonly used in trigonometry courses.

5. Provide the decimal approximation as the exact radical form is excessively complex.

Final Answer

sin(28^∘)≈0.46947156

Want more problems? Check here!