Find the Exact Value cos(360 degrees )

Problem

cos(360^∘)

Solution

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

2. Determine the terminal side of the angle. The terminal side of 360^∘ lies on the positive x-axis, which is the same position as 0^∘

3. Find the coordinates of the point on the unit circle at this angle. The point on the unit circle at 360^∘ is (1,0)

4. Apply the definition of the cosine function. On the unit circle, cos(θ) is equal to the x-coordinate of the point.

5. Extract the value from the coordinates. Since the x-coordinate is 1 the value of the cosine is 1

Final Answer

cos(360^∘)=1

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