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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