Find the Value Using the Unit Circle sin((3pi)/2)

Problem

sin((3*π)/2)

Solution

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

2. Locate the terminal side of the angle. This angle lies on the negative yaxis.

3. Determine the coordinates of the point where the terminal side intersects the unit circle. The coordinates at (3*π)/2 are (0,−1)

4. Apply the definition of the sine function on the unit circle. For any point (x,y) on the unit circle, sin(θ)=y

5. Extract the ycoordinate from the point (0,−1)

Final Answer

sin((3*π)/2)=−1

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