You are given that sin(-t) = .
It means that sin(t) = . (Sine is an odd function).
Hence, csc(t) = = = . ANSWER
Solved.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website! you are given that sin(-t) = 6/7.
you want to define csc(t) in terms of sin(-t).
by definition, csc(t) = 1/sin(t).
it can be shown that sin(-t) = -sin(t).
multiply both sides of this equation by -1 to get -sin(-t) = sin(t).
replace sin(t) with -sin(-t) in the equation of csc(t) = 1/sin(t) to get:
csc(t) = 1/-sin(-t).
it can be shown that 1/-sin(-t) is the same as -1/sin(-t).
therefore:
csc(t) = -1/sin(-t).
that should be your solution.
csc(t) is defined in terms of sin(-t)
to confirm that this is true, do the following:
start with sin(-t) = 6/7
solve for -t to get:
-t = arcsin(6/7) = 58.99728087 degrees.
multiply both sides of this equation by -1 to get:
t = -58.99728087.
you have:
-t = 58.99728087 degrees.
t = -58.99728087 degrees.
csc(t) = 1/sin(t) = 1/sin(-58.99728087) = -1.16666666.....
csc(t) = -1/sin(-t) = -1/sin(58.99728087) = -1.6666666....
this confirms that csc(t) = -1/sin(-t)