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Homework Statement
Use properties of the trigonometric functions to find the exact value of each expression. Do not use a calculator
sin (-pi/12) csc (25 pi)/12
Homework Equations
sin (negative angle) = - sin (angle)
csc theta = (sin theta)^-1 = 1/(sin theta)
The Attempt at a Solution
Ok there is obviously some sort of property of trig identies I do not know so I'm struggling here...
sin(-pi/12) csc( (25 pi)/12 ) = (- sin(pi/12) )/(sin( (25 pi)/12))
know if I'm correct I just treat them as exponents correct? so I subtract them
- sin( (pi/12) - ( (25 pi)/12 )
- sin( (-24 pi)/12 )
+ sin( (24 pi)/12
sin 2 pi = 0
OK THIS IS WRONG I put this into my calculator and i get negative one. I postulated for like two hours on how to do this. I think I figuered it out but am not sure why it works can someone please explain it to me...
ok I start out here
sin(-pi/12) csc( (25 pi)/12 ) = (- sin(pi/12) )/(sin( (25 pi)/12))
then
- sin( (pi/12) - ( (25 pi)/12 )
- sin( (24 pi)/12 )
if i just ignore the negative sign next to the 24... something here is wrong with what I'm doing HELP
- sin( (24 pi)/12 )
now I take the recipical but leave the pi on top of the angle not sure why or why i leave pi on top
- sin( (12 pi)/24
simplify
- sin( pi/2
pi/2 is ninety degrees which has the coordinates (0,1) and sense sine is equal to the y cordinate I get one but sense it's the opposite i get negative 1 as my answer which is correct
So I obviously have no idea how to really do this problem if someone could tell me how to do this that would be great. There isn't really much I can do because I'm obviously don't know some property or something here.
Thanks