Find the Exact Value sin(1/4*pi)

Problem

sin(1/4*π)

Solution

1. Identify the angle in standard radians. The expression 1/4*π is equivalent to π/4 radians.

2. Convert the angle to degrees if necessary to recognize it on the unit circle. Since π radians equals 180 then π/4 radians equals 45

3. Recall the coordinates of the unit circle for the angle π/4 At this position, the xcoordinate and ycoordinate are equal.

4. Apply the definition of the sine function on the unit circle, where sin(θ) corresponds to the ycoordinate.

5. Determine the exact value. For θ=π/4 the ycoordinate is √(,2)/2

Final Answer

sin(1/4*π)=√(,2)/2

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