Find the Exact Value sin(-180 degrees )

Problem

sin(−180^∘)

Solution

1. Identify the angle on the unit circle. The angle −180^∘ represents a clockwise rotation of 180^∘ from the positive x-axis.

2. Determine the terminal side. A rotation of −180^∘ lands on the negative x-axis, which is the same position as 180^∘

3. Find the coordinates of the point on the unit circle at this angle. The coordinates at 180^∘ (or −180^∘ are (−1,0)

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

5. Extract the value. Since the y-coordinate is 0 the sine of the angle is 0

Final Answer

sin(−180^∘)=0

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