<PRE><B>Question 884444</B>
csc660= 1/sin 660 
note that 660 - 360 = 300
300 degrees is in the fourth quadrant and its reference angle is 360 - 300 = 60 degrees
note that the sine function in quadrant 4 is negative
csc660 = 1/sin 660 = 1 / -sin 60 
now use a right triangle with hypotenuse 2, altitude 1 and base is square root of 3
60 degree angle is opposite the base 
therefore the sin 60 = square root (3) / 2 
now we can write
csc660 = 1 / (-square root (3) / 2) = 2 / -square root(3)
multiply the numerator and denominator by square root(3)
csc660 = (-2*square root(3)) / 3

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