Simplify sin(100)

Problem

sin(100)

Solution

1. Identify the angle and the goal. The angle is 100 which is in the second quadrant (90<100<180.

2. Apply the reduction formula for the second quadrant, which states sin(θ)=sin(180−θ)

3. Calculate the reference angle by subtracting 100 from 180

180−100=80

4. Rewrite the expression using the reference angle. Since sine is positive in the second quadrant, the value remains positive.

sin(100)=sin(80)

5. Apply the cofunction identity if further simplification is desired, where sin(θ)=cos(90−θ)

90−80=10

sin(80)=cos(10)

Final Answer

sin(100)=sin(80)

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