Find the Exact Value sin(-90 degrees )

Problem

sin(−90)

Solution

1. Identify the angle on the unit circle. The angle −90 represents a clockwise rotation of 90 from the positive x-axis.

2. Determine the terminal side of the angle. A rotation of −90 ends on the negative y-axis.

3. Find the coordinates of the point on the unit circle at this position. The coordinates are (0,−1)

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 −1 the sine of the angle is −1

Final Answer

sin(−90)=−1

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