Find the Exact Value sin(110)

Problem

sin(110^∘)

Solution

1. Identify the angle and the required operation. The task is to find the exact value of sin(110^∘)

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

3. Substitute 110^∘ into the identity to find the equivalent reference angle.

sin(110^∘)=sin(180^∘−110^∘)

4. Simplify the expression to find the sine of the resulting angle.

sin(110^∘)=sin(70^∘)

5. Determine if a simpler exact value exists. Since 70^∘ is not a standard unit circle angle (like 30^∘ 45^∘ or 60^∘, the exact value is expressed in terms of the sine function.

Final Answer

sin(110^∘)=sin(70^∘)

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