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Popular >

cot(5/4 pi)

Solution

cot (\frac{5}{4} π)

Solution

1

Solution steps

cot (\frac{5}{4} π)

Simplify:

\frac{5}{4} π = \frac{5 π}{4}

\frac{5}{4} π

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{5 π}{4}

= cot (\frac{5 π}{4})

cot (\frac{5 π}{4}) = cot (\frac{π}{4})

cot (\frac{5 π}{4})

Rewrite

\frac{5 π}{4}

as

π + \frac{π}{4}

= cot (π + \frac{π}{4})

Apply the periodicity of

cot

:

cot (x + π) = cot (x)

cot (π + \frac{π}{4}) = cot (\frac{π}{4})

= cot (\frac{π}{4})

= cot (\frac{π}{4})

Use the following trivial identity:

cot (\frac{π}{4}) = 1

cot (\frac{π}{4})

cot (x)

periodicity table with

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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

= 1

= 1

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Frequently Asked Questions (FAQ)

What is the value of cot(5/4 pi) ?
The value of cot(5/4 pi) is 1