document.write( "Question 1203702: Use the given value to evaluate each function.
\n" ); document.write( "sin(−t) = 6/7\r
\n" ); document.write( "\n" ); document.write( "Write csc(t) in terms of the sine function.
\n" ); document.write( "csc(t) = \n" ); document.write( "
Algebra.Com's Answer #839490 by Theo(13342)\"\" \"About 
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you are given that sin(-t) = 6/7.
\n" ); document.write( "you want to define csc(t) in terms of sin(-t).
\n" ); document.write( "by definition, csc(t) = 1/sin(t).
\n" ); document.write( "it can be shown that sin(-t) = -sin(t).
\n" ); document.write( "multiply both sides of this equation by -1 to get -sin(-t) = sin(t).
\n" ); document.write( "replace sin(t) with -sin(-t) in the equation of csc(t) = 1/sin(t) to get:
\n" ); document.write( "csc(t) = 1/-sin(-t).
\n" ); document.write( "it can be shown that 1/-sin(-t) is the same as -1/sin(-t).
\n" ); document.write( "therefore:
\n" ); document.write( "csc(t) = -1/sin(-t).
\n" ); document.write( "that should be your solution.
\n" ); document.write( "csc(t) is defined in terms of sin(-t)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "to confirm that this is true, do the following:
\n" ); document.write( "start with sin(-t) = 6/7
\n" ); document.write( "solve for -t to get:
\n" ); document.write( "-t = arcsin(6/7) = 58.99728087 degrees.
\n" ); document.write( "multiply both sides of this equation by -1 to get:
\n" ); document.write( "t = -58.99728087.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "you have:
\n" ); document.write( "-t = 58.99728087 degrees.
\n" ); document.write( "t = -58.99728087 degrees.
\n" ); document.write( "csc(t) = 1/sin(t) = 1/sin(-58.99728087) = -1.16666666.....
\n" ); document.write( "csc(t) = -1/sin(-t) = -1/sin(58.99728087) = -1.6666666....
\n" ); document.write( "this confirms that csc(t) = -1/sin(-t)\r
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