Find the Exact Value sin(100)

Problem

sin(100^∘)

Solution

1. Identify the angle and the required operation. The task asks for the exact value of sin(100^∘)

2. Apply the supplementary angle identity, which states sin(θ)=sin(180^∘−θ)

3. Substitute the value θ=100^∘ into the identity to find an equivalent expression in the first quadrant.

sin(100^∘)=sin(180^∘−100^∘)

sin(100^∘)=sin(80^∘)

4. Determine if a simpler exact form exists. Since 80^∘ is not a standard reference angle (like 30^∘ 45^∘ or 60^∘, the exact value is typically expressed in terms of the sine or cosine of its reference angle, or using power-reduction or sum-to-product formulas which do not result in simpler radicals.

Final Answer

sin(100^∘)=sin(80^∘)

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