precalc
posted by sarah .
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
Respond to this Question
Similar Questions

Math
1)A piano tuner uses a tuning fork. If middle C has a frequency of 264 vibrations per second, write an equation in the form d=sinw(t) for the simple harmonic motion. 2) Verify the identity tan^2Xcot^2X/tanX+cotX=tanXcotX I'm not … 
CALC HW
FIND THE X VALUES OF ALL POINTS, 2PI LESS THAN OR EQUAL TO X LESS THAN OR EQUAL TO 2PI, WHERE Y=X+B IS TANGENT TO Y=X+BSINX. I KNOW THE ANSWER IS PI/2 AND 3PI/2, BUT WHY AREN'T THEY PLUS OR MINUS. If they are tangent, they have the … 
calculus
express in sinx 1 1  +  cscx + cotx cscx  cotx and express in cosx 1 + cot x   sin^2x cscx = 1/sinx so what do i do w. that extra one on the top!? 
trig
express this in sinx (1/ cscx + cotx )+ (1/cscx cotx) i got 2sinx is that right? 
trigonometry
How do you find: cot(5pie/4)? you have to know that cotx = 1/tanx so you could just trustfully change your calculator to radians enter 5*pi/4, press =, press +/, then press Tan, =, then the 1/x key you should get 1 or... you could 
drwls
My previous question: Verify that (secx/sinx)*(cotx/cscx)=cscx is an identity. (secx/sinx)*(cotx/cscx) = (secx/cscx)(cotx/sinx) = (sinx/cosx)*cotx*(1/sinx) "The last steps should be obvious" Not to me. I can convert (sinx/cosx) to … 
PreCalculus
Find a numerical value of one trigonometric function of x if tanx/cotx  secx/cosx = 2/cscx a) cscx=1 b) sinx=1/2 c)cscx=1 d)sinx=1/2 
PreCalc/Math
Given cos x=2/3 and 3pi/2<x<2pi, find the exact value of cos2x? 
Math
Im really struggling with these proving identities problems can somebody please show me how to do these? 
Math
Im really struggling with these proving identities problems can somebody please show me how to do these?