What is the value of csc(pi/4) ?

The value of csc(pi/4) is square root of 2

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csc(pi/4)

csc (\frac{π}{4})

2

Decimal Notation

1.41421 \dots

Solution steps

csc (\frac{π}{4})

Use the following trivial identity:

csc (\frac{π}{4}) = 2

csc (\frac{π}{4})

csc (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

= 2

= 2

\frac{cos ( 2 x ) - cos ( 4 x )}{sin ( 2 x ) + sin ( 4 x )} = tan (x)

sec (\frac{7 π}{4})

sin (- \frac{11 π}{12})

arcsin (0)

arccos (- \frac{3}{2})