posted by sarah .
Can someone help me find the exact value of 4csc(3pi/4)-cot(-pi/4)?
cscx = 1/sinx
If you find it easier to conceptualize in degrees, realize that pi/4 radians is 45º and 3pi/4 is then 135º
If you know the CAST rule, it is easy to see that -pi/4 is in the fourth quadrant and tan(-pi/4) or tan(-45º) = -1
therefore cot(-pi/4) = -1
3pi/4 or 135º is in the second quadrant where the sine is positive.
so sin(3pi/4) = 1/(√2)
then csc(3pi/4) = √2
and 4csc(3pi/4) = 4√2
so the exact value of 3csc(3pi/4) - cot(-pi/4)
= 4√2 + 1