What is the value of cos((4pi)/9)cos(pi/9)+sin((4pi)/9)sin(pi/9) ?

The value of cos((4pi)/9)cos(pi/9)+sin((4pi)/9)sin(pi/9) is 1/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos((4pi)/9)cos(pi/9)+sin((4pi)/9)sin(pi/9)

cos (\frac{4 π}{9}) cos (\frac{π}{9}) + sin (\frac{4 π}{9}) sin (\frac{π}{9})

\frac{1}{2}

Decimal Notation

0.5

Solution steps

cos (\frac{4 π}{9}) cos (\frac{π}{9}) + sin (\frac{4 π}{9}) sin (\frac{π}{9})

Rewrite using trig identities:

cos (\frac{π}{3})

cos (\frac{4 π}{9}) cos (\frac{π}{9}) + sin (\frac{4 π}{9}) sin (\frac{π}{9})

Use the Angle Difference identity:

cos (s) cos (t) + sin (s) sin (t) = cos (s - t)

= cos (\frac{4 π}{9} - \frac{π}{9})

Simplify:

\frac{4 π}{9} - \frac{π}{9} = \frac{π}{3}

\frac{4 π}{9} - \frac{π}{9}

Apply rule

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

= \frac{4 π - π}{9}

Add similar elements:

4 π - π = 3 π

= \frac{3 π}{9}

Cancel the common factor:

3

= \frac{π}{3}

= cos (\frac{π}{3})

= cos (\frac{π}{3})

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

cos (\frac{π}{3})

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{1}{2}

= \frac{1}{2}

cot (\frac{5}{4} π)

arcsin (0.367)

\frac{tan ( 10 6 ^{\circ} ) + tan ( - 6 1 ^{\circ} )}{1 - tan ( 10 6 ^{\circ} ) tan ( - 6 1 ^{\circ} )}

- csc^{2} (\frac{7 π}{6})

sin^{2} (6 0^{\circ}) + tan^{2} (6 0^{\circ}) - csc^{2} (3 0^{\circ})

What is the value of cos((4pi)/9)cos(pi/9)+sin((4pi)/9)sin(pi/9) ?
The value of cos((4pi)/9)cos(pi/9)+sin((4pi)/9)sin(pi/9) is 1/2