Find the Exact Value cos(180 degrees )

Problem

cos(180)

Solution

1. Identify the position of the angle 180 on the unit circle.

2. Determine the coordinates (x,y) of the point where the terminal side of the angle intersects the unit circle.

3. Recall that for any point (x,y) on the unit circle, cos(θ)=x

4. Observe that at 180 the point on the unit circle is (−1,0)

5. Conclude that the xcoordinate is −1

Final Answer

cos(180)=−1

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