Simplify cos(180)

Problem

cos(180^∘)

Solution

1. Identify the angle on the unit circle. The angle 180^∘ (or π radians) corresponds to the point on the far left of the unit circle.

2. Determine the coordinates of the point. On a unit circle, the coordinates at 180^∘ are (−1,0)

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

4. Substitute the x-coordinate into the function to find the value.

Final Answer

cos(180^∘)=−1

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