Ok I do not know how to do this problem. I know that csc is simply sin^-1
sin (- pi/12) csc ( (37 pi)/12
ok now I know this also
sin (- pi /12 ) = - sin ( pi/12)
not really sure how that helps
I don't know were to go from here
( - sin (pi/12) )/(sin ( (25 pi)/12 ) )
I thought I answered this.
Remember sin Theta=sin(theta+2PI)
and, remember that sin(-theta)=-sinTheta
so
Sin(-PI/12)=-sin(PI/12)
and lastly, sin(theta)=-sin(theta+PI)
Now, to the task
sin(-PI/12)=-sin(PI/12)= + sin(PI/12+PI)
= sin(13PI/12)=sin(13PI/12+2PI)
= sin(13PI/12+24pi/12)=sin 37PI/12
Now you have
sin(37PI/12)*csc(37pi/12)=1
Why did you take the negative sign out?
sin(-PI/12)=-sin(PI/12)
I understand this
why are we adding pi to the denomenator
I udner stand that sin (theta) = sin (theta + 2pi)
= + sin(PI/12+PI)
I don't understand that
= sin(13PI/12)
how did we get thirteen ontop?
=sin(13PI/12+2PI)
I understood that
= sin(13PI/12+24pi/12)
so you just rewrote 2pi in therms of a twelth (24pi)/12 makes sense
=sin 37PI/12
ok simplified it
ok so if you can explain the steps i don't understand that would be great thanks!!!!
sin(PI/12 + PI) is not adding it to the denominator, If I wanted to add it to the denominator..
Sin(PI/(12+PI))
So
Sin(PI/12 + PI)=sin (PI/12 + 12PI/12)=
sin(13PI/12)
go back and reread what I did.
ok then everything makes sense you just added pi to make it positive and then everything else makes perfect sense but allows you just to add pi to make it positive?
will I do that on my calculator and get the same answer so I guess it's some kind of property of sin...???
so then I can state this?
for sin (theta)
I can add pi to theta and still get the same answer??? this would appear to be true
does this also hold true for cosine and tangent?
So then
sin - theta + pi = sin theta
cos - theta + pi = cos -theta
ok then I can just simply add pi to it to change it's sign (positive or negative) just like I could with anything without changing it's value????
so we can just simply add pi to theta because it dosen't change its value but it change it's sign which we can do because...
I put this into my calculator and get negative one not positive one
(sin(-pi/12))(sin((25pi)/12))^-1
To simplify the expression (- sin(pi/12))/(sin((25 pi)/12)), we can start by using the fact that sin(-θ) = -sin(θ).
Given that sin(-pi/12) = -sin(pi/12), the expression can be rewritten as:
(-sin(pi/12))/(sin((37 pi)/12))
Now, let's focus on the denominator sin((37 pi)/12). To simplify it, we need to evaluate sin((37 pi)/12).
To find the value, we can use the periodicity property of sine function. The sine function repeats its values every 2π radians, so we can write:
sin((37 pi)/12) = sin((37 pi)/12 - 2π)
Since 2π is equivalent to 24π/12, we can simplify the expression further:
sin((37 pi)/12) = sin((37 pi)/12 - 24π/12)
Now, let's simplify the angle inside the sin function:
(37 pi)/12 - 24π/12 = (37 pi - 24π)/12 = (13 pi)/12
Therefore, sin((37 pi)/12) is equivalent to sin((13 pi)/12).
Now, we have the simplified expression: (-sin(pi/12))/(sin((13 pi)/12))
By substituting these values, we have:
(-sin(pi/12))/(sin((13 pi)/12))
=(-sin(pi/12))/(sin((13 pi)/12))
Now, you can evaluate this expression using a calculator or a trigonometric identity for sin(pi/12). If you want to calculate it, remember to check if your calculator is in radians or degrees mode.