multiply that by 180 and divide it by pi and you will get the equivalent angle in degrees.
the equivalent angle in degrees is equla to 3pi/2 * 180/pi = 270 degrees.
that angle is in the fourth quadrant.
the sine of any angle in the fourth quadrant is negative.
this is because the value of y in the triangle formed is negative and since sine is defined as opposite side divided by hypotenuse, and since the hypotenuse is always positive, you get sine of the angle in the fourth quadrant is equal to the side opposite divided by the hypotenuse which involves a negative value divided by a positive value which results in a negative value.
the angle in the fourth quadrant is equivalent to the corresponding angle in the first qaadrant except that it is negative.
the equivalent angle in the first quadrant is calculated as 360 - 270 = 90.
the equivalent angle in the first quadrant, called the reference angle, is 90 degrees.
the sine of 90 degrees is 1.
the sine of 270 degrees is the same value only negative.
that makes the sine of 270 degrees equal to -1.
i did this in degrees, but the same concept applies to radians.
270 degrees is equivalent to 3pi/2.
the corresponding angle in the first quadrant is equal to 2pi - 3pi/2 which becomes 4pi/2 - 3pi/2 which becomes pi/2 which is equal to 90 degrees.
if you graphed the sine function in radians, you would see that the value of the sine of 270 degrees is -1.
