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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