Find the value of $csc(frac{pi}{4})$ using the unit circle.

$ \text{Step 1: Determine the sine of } \frac{\pi}{4} $

$ \sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2} $

$ \text{Step 2: Use the definition of cosecant: } csc(\theta) = \frac{1}{\sin(\theta)} $

$ csc(\frac{\pi}{4}) = \frac{1}{\sin(\frac{\pi}{4})} = \frac{1}{\frac{\sqrt{2}}{2}} = \frac{2}{\sqrt{2}} = \sqrt{2} $

$ ext{Step 1: Calculate } sin(frac{pi}{4}) $

$ sin(frac{pi}{4}) = frac{sqrt{2}}{2} $

$ ext{Step 2: Use the definition of cosecant: } csc( heta) = frac{1}{sin( heta)} $

$ csc(frac{pi}{4}) = frac{1}{sin(frac{pi}{4})} $

$ csc(frac{pi}{4}) = frac{1}{frac{sqrt{2}}{2}} = sqrt{2} $

$ ext{Given: } sin(frac{pi}{4}) = frac{sqrt{2}}{2} $

$ ext{Hence, } csc(frac{pi}{4}) = frac{1}{sin(frac{pi}{4})} = sqrt{2} $

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