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How to find the value of #csc ((3pi)/4)#?

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Jun 5, 2015

The angle #((3pi)/4)# is in Quadrant 2 with a reference angle of #pi/4#

#sin(pi/4) = 1/sqrt(2)##color(white)("XXXX")#(it's one of the standard angles)

and in Quadrant 2, #sin(x)# is positive, so
#color(white)("XXXX")##sin((3pi)/4) = sin(pi/4) = 1/sqrt(2)#

#csc(x) = 1/(sin(x))#

So
#csc((3pi)/4) = sqrt(2)#

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