Questions: Please evaluate. csc (π/4) (A) Undefined (B) 1 (C) √2 (D) 2 (E) 2√3/3

Solution Steps

The cosecant function is defined as the reciprocal of the sine function: \[ \csc \theta = \frac{1}{\sin \theta} \]

The sine of \(\frac{\pi}{4}\) radians is: \[ \sin \frac{\pi}{4} = \frac{\sqrt{2}}{2} \]

Using the definition of cosecant and the value of \(\sin \frac{\pi}{4}\): \[ \csc \frac{\pi}{4} = \frac{1}{\sin \frac{\pi}{4}} = \frac{1}{\frac{\sqrt{2}}{2}} = \frac{2}{\sqrt{2}} = \sqrt{2} \]

Final Answer