Find the Exact Value sin(43)

Problem

sin(43^∘)

Solution

1. Identify the nature of the angle. The angle 43^∘ is not a standard reference angle (such as 0^∘,30^∘,45^∘,60^∘,90^∘ for which exact values are typically expressed in simple radicals.

2. Determine if a trigonometric identity applies. While 43^∘ can be expressed as 45^∘−2^∘ the exact value for sin(2^∘) is not a simple algebraic number, meaning the result cannot be simplified into a standard radical form.

3. Conclude the exact representation. In trigonometry, if an angle does not correspond to a standard multiple of 3^∘ or 1.5^∘ that allows for radical expansion, the exact value is simply the expression itself.

Final Answer

sin(43^∘)=sin(43^∘)

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