Posted by **sarah** on Saturday, May 5, 2007 at 4:10pm.

Can someone help me find the exact value of 4csc(3pi/4)-cot(-pi/4)?

Thanks!

cotx =1/tanx

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

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