What is the value of cos((6pi)/8) ?

The value of cos((6pi)/8) is -(sqrt(2))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos((6pi)/8)

cos (\frac{6 π}{8})

- \frac{2}{2}

Decimal Notation

- 0.70710 \dots

Solution steps

cos (\frac{6 π}{8})

Simplify:

\frac{6 π}{8} = \frac{3 π}{4}

\frac{6 π}{8}

Cancel the common factor:

2

= \frac{3 π}{4}

= cos (\frac{3 π}{4})

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

cos (\frac{3 π}{4})

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} 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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= - \frac{2}{2}

= - \frac{2}{2}

sin (15 9^{\circ})

tan (15 0^{\circ}) \cdot sin (31 5^{\circ})

2 \cdot 3 \cdot 214 \cdot sin (\frac{16 2 ^{\circ}}{2})

tan (\frac{- 8}{2})

10 cos (\frac{π}{4}) - 10 sin (\frac{π}{4})