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

Problem

cos((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. An angle of (3*π)/2 points directly downward along the negative yaxis.

3. Determine the coordinates of the point where the terminal side intersects the unit circle. This point is (0,−1)

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

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

Final Answer

cos((3*π)/2)=0

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