Find the Value Using the Unit Circle sin(180)

Problem

sin(180)

Solution

1. Identify the angle on the unit circle. The angle 180 corresponds to a half-rotation around the circle starting from the positive x-axis.

2. Determine the coordinates of the point on the unit circle at 180 This point lies on the negative x-axis.

3. Recall the coordinates for 180 are (−1,0)

4. Apply the definition of the sine function on the unit circle, where sin(θ) is equal to the y-coordinate of the point.

5. Extract the y-coordinate from the point (−1,0) which is 0

Final Answer

sin(180)=0

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