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How to find the value of $csc (\frac{3 π}{4})$ $csc ((3pi)/4)$ ?

1 Answer

Jun 5, 2015

The angle $(\frac{3 π}{4})$ $((3pi)/4)$ is in Quadrant 2 with a reference angle of $\frac{π}{4}$ $pi/4$

$sin (\frac{π}{4}) = \frac{1}{\sqrt{2}}$ $sin(pi/4) = 1/sqrt(2)$ $XXXX$ $color(white)("XXXX")$ (it's one of the standard angles)

and in Quadrant 2, $sin (x)$ $sin(x)$ is positive, so
$XXXX$ $color(white)("XXXX")$ $sin (\frac{3 π}{4}) = sin (\frac{π}{4}) = \frac{1}{\sqrt{2}}$ $sin((3pi)/4) = sin(pi/4) = 1/sqrt(2)$

$csc (x) = \frac{1}{sin (x)}$ $csc(x) = 1/(sin(x))$

So
$csc (\frac{3 π}{4}) = \sqrt{2}$ $csc((3pi)/4) = sqrt(2)$

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