SOLUTION: Use the given value to evaluate each function. sin(−t) = 6/7 Write csc(t) in terms of the sine function. csc(t) =

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Question 1203702: Use the given value to evaluate each function.
sin(−t) = 6/7
Write csc(t) in terms of the sine function.
csc(t) =
Found 3 solutions by Edwin McCravy, ikleyn, Theo:
Answer by Edwin McCravy(20060) About Me  (Show Source):
Answer by ikleyn(52810) About Me  (Show Source):
You can put this solution on YOUR website!
.

You are given that  sin(-t) = 6%2F7.

It means that sin(t) = -6%2F7.   (Sine is an odd function).


Hence,  csc(t) = 1%2Fsin%28t%29 = 1%2F%28%28-6%2F7%29%29 = -7%2F6.    ANSWER

Solved.



Answer by Theo(13342) About Me  (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)