The value of sin(3π/2) is -1.
Here's how to calculate it using the unit circle:
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Understanding the Unit Circle: The unit circle is a circle with a radius of 1 centered at the origin (0,0) of the Cartesian plane. Angles are measured counterclockwise from the positive x-axis.
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Locating 3π/2 on the Unit Circle: The angle 3π/2 (which is 270 degrees) corresponds to the point (0, -1) on the unit circle.
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Sine as the y-coordinate: On the unit circle, the sine of an angle is represented by the y-coordinate of the point where the terminal side of the angle intersects the circle.
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Determining sin(3π/2): Since the coordinates of the point corresponding to 3π/2 are (0, -1), the y-coordinate is -1. Therefore, sin(3π/2) = -1.
