Find the Value Using the Unit Circle sin(pi/4)

Problem

sin(π/4)

Solution

1. Identify the angle on the unit circle. The angle is given in radians as π/4

2. Convert the angle to degrees if necessary to visualize. Since π radians equals 180 then π/4 is equal to 45

3. Locate the coordinates (x,y) at π/4 on the unit circle. At this position, the point is (√(,2)/2,√(,2)/2)

4. Apply the definition of the sine function on the unit circle. The value of sin(θ) corresponds to the ycoordinate of the point.

5. Extract the ycoordinate from the point (√(,2)/2,√(,2)/2)

Final Answer

sin(π/4)=√(,2)/2

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