What is the value of cot(pi+pi/4) ?

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cot(pi+pi/4)

cot (π + \frac{π}{4})

1

Solution steps

cot (π + \frac{π}{4})

Simplify:

π + \frac{π}{4} = \frac{5 π}{4}

π + \frac{π}{4}

Convert element to fraction:

π = \frac{π 4}{4}

= \frac{π 4}{4} + \frac{π}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{π 4 + π}{4}

Add similar elements:

4 π + π = 5 π

= \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}

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

sin (126.8 7^{\circ})

\frac{2 cos ( \frac{π}{4} ) - sin ( \frac{3 π}{4} )}{1 - cos ( \frac{π}{4} )}

arcsin (\frac{3}{6})

cos (\frac{6}{8})

6 + 3 cos (\frac{π}{4})