What is the value of csc((17pi)/4) ?

The value of csc((17pi)/4) is square root of 2

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csc((17pi)/4)

csc (\frac{17 π}{4})

2

Decimal Notation

1.41421 \dots

Solution steps

csc (\frac{17 π}{4})

csc (\frac{17 π}{4}) = csc (\frac{π}{4})

csc (\frac{17 π}{4})

Rewrite

\frac{17 π}{4}

2 π \cdot 2 + \frac{π}{4}

= csc (2 π 2 + \frac{π}{4})

Apply the periodicity of

csc

csc (x + 2 π \cdot k) = csc (x)

csc (2 π \cdot 2 + \frac{π}{4}) = csc (\frac{π}{4})

= csc (\frac{π}{4})

= 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

arccos (\frac{5}{12})

2 sec (0)

tan (- 24 0^{\circ})

5 sin (2 π)

1 - sin (0)

What is the value of csc((17pi)/4) ?
The value of csc((17pi)/4) is square root of 2