Evaluate. Write your answer in simplified, rationalized form. Do not round.
csc
𝜋
4
Recall that csc is the reciprocal of sin. Therefore:
csc(𝜋/4) = 1/sin(𝜋/4)
We know that sin(𝜋/4) = (√2)/2. Therefore:
csc(𝜋/4) = 1/((√2)/2)
Simplifying by rationalizing the denominator:
csc(𝜋/4) = 2/√2
Simplifying further by simplifying the radical:
csc(𝜋/4) = 2√2/2
Finally, simplifying by canceling out the 2's:
csc(𝜋/4) = √2