Find the Value Using the Unit Circle cos(360)

Problem

cos(360^∘)

Solution

1. Identify the angle on the unit circle. An angle of 360^∘ represents one full counter-clockwise rotation around the circle.

2. Determine the terminal side of the angle. The angle 360^∘ is coterminal with 0^∘ meaning its terminal side lies along the positive x-axis.

3. Locate the coordinates of the point where the terminal side intersects the unit circle. For 360^∘ this point is (1,0)

4. Apply the definition of the cosine function on the unit circle. The value of cos(θ) is equal to the x-coordinate of the intersection point.

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

Final Answer

cos(360^∘)=1

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