Evaluate sin((3pi)/2)

Problem

sin((3*π)/2)

Solution

1. Identify the angle on the unit circle. The angle (3*π)/2 radians corresponds to 270

2. Determine the coordinates of the point on the unit circle at this angle. The point is located on the negative y-axis.

3. Locate the specific coordinates (x,y) which are (0,−1)

4. Apply the definition of the sine function on the unit circle, where sin(θ)=y

5. Extract the y-coordinate from the point (0,−1)

Final Answer

sin((3*π)/2)=−1

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