Simplify sin(80)

Problem

sin(80)

Solution

1. Identify the expression as the sine of an angle measured in degrees.

2. Determine if the angle corresponds to a standard value on the unit circle. Since 80 is not a multiple of 30 or 45 it does not have a simple exact radical form like 1/2 or √(,3)/2

3. Express the value using cofunction identities if needed. The sine of an angle is equal to the cosine of its complement.

4. Apply the identity sin(θ)=cos(90−θ)

sin(80)=cos(90−80)

sin(80)=cos(10)

Final Answer

sin(80)=cos(10)

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