SOLUTION: Hi! How could I solve without using a calculator: csc(-9Π/4) = ? Thanks!

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Question 1089973: Hi!
How could I solve without using a calculator:
csc(-9Π/4) = ?
Thanks!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
sin%28x%29,+cos%28x%29,+sec%28x%29,+csc%28x%29 all have a period of 2pi so,
-%289%2F4%29pi%2B2pi=%28-9%2F4%2B8%2F4%29pi=-pi%2F4
So,
sin%28-%289%2F4%29pi%29=sin%28-pi%2F4%29=-sin%28pi%2F4%29=-sqrt%282%29%2F2
Since,
csc%28-pi%2F4%29=1%2Fsin%28-pi%2F4%29
Then,
csc%28-pi%2F4%29=-2%2Fsqrt%282%29=-sqrt%282%29
So,
highlight_green%28csc%28-%289%2F4%29pi%29=-sqrt%282%29%29