How do you solve $csc (\frac{19 π}{4}) = \sqrt{2}$ $csc((19pi)/4)=sqrt2$ ?

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How do you solve $csc (\frac{19 π}{4}) = \sqrt{2}$ $csc((19pi)/4)=sqrt2$ ?

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Answer 1 · 2017-03-19T15:41:01

Trig table of special arcs and unit circle give:
$sin (\frac{19 π}{4}) = sin (\frac{3 π}{4} + 4 π) = sin (\frac{3 π}{4}) = \frac{\sqrt{2}}{2}$ $sin ((19pi)/4) = sin ((3pi)/4 + 4pi) = sin ((3pi)/4) = sqrt2/2$
Therefore:
$csc (\frac{18 π}{4}) = \frac{1}{sin (\frac{3 π}{4})} = \frac{2}{\sqrt{2}} = \sqrt{2}$ $csc ((18pi)/4) = 1/(sin ((3pi)/4)) = 2/sqrt2 = sqrt2$ . Proved.

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How do you solve $csc (\frac{19 π}{4}) = \sqrt{2}$ $csc((19pi)/4)=sqrt2$ ?

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How do you solve csc((19pi)/4)=sqrt2csc(19π4)=√2csc((19pi)/4)=sqrt2?

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How do you solve $csc (\frac{19 π}{4}) = \sqrt{2}$ $csc((19pi)/4)=sqrt2$ ?