What is the exact value of csc 5pi/4?

If you can give me steps or examples to how to get the exact value that will be great.

2 Answers

  • csc 5pi/4

    =1/sin(pi+pi/4) = 1/(-sinpi/4) = -1/(1/sqrt2 )= -sqrt 2 = -1.414

  • sqrt(2)

    Why?

    First we find the reciprocal of csc, which is: sin(5pi/4),

    Then just flip it.

    We know sin(5pi/4) = (sqrt2)/2

    So csc(5pi/4) is simply: 2/(sqrt2) or simplified as (sqrt2)

    You can check these answers on a calculator for thoroughness, i did...and both decimals came out to be equal.

    Good luck!

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