Find the Exact Value sin(360)

Problem

sin(360^∘)

Solution

1. Identify the angle in the unit circle. The angle 360^∘ represents one full rotation around the circle, which is coterminal with 0^∘

2. Determine the coordinates on the unit circle. At 360^∘ (or 0^∘, the point on the unit circle is (1,0)

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

4. Extract the ycoordinate from the point (1,0)

Final Answer

sin(360^∘)=0

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