What is the value of cos(100)cos(40)+sin(100)sin(40) ?

The value of cos(100)cos(40)+sin(100)sin(40) is 1/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(100)cos(40)+sin(100)sin(40)

cos (10 0^{\circ}) cos (4 0^{\circ}) + sin (10 0^{\circ}) sin (4 0^{\circ})

\frac{1}{2}

Decimal Notation

0.5

Solution steps

cos (10 0^{\circ}) cos (4 0^{\circ}) + sin (10 0^{\circ}) sin (4 0^{\circ})

Rewrite using trig identities:

cos (6 0^{\circ})

cos (10 0^{\circ}) cos (4 0^{\circ}) + sin (10 0^{\circ}) sin (4 0^{\circ})

Use the Angle Difference identity:

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

= cos (10 0^{\circ} - 4 0^{\circ})

Simplify

= cos (6 0^{\circ})

= cos (6 0^{\circ})

Use the following trivial identity:

cos (6 0^{\circ}) = \frac{1}{2}

cos (6 0^{\circ})

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} 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}

tan^{2} (1 5^{\circ})

\frac{100}{cos ( 3 0 ^{\circ} )}

1 - cos (\frac{3 π}{4})

sin (21 7^{\circ})

\frac{sin ( 12 0 ^{\circ} )}{tan ( 4 5 ^{\circ} ) + sin ( 21 0 ^{\circ} ) cos ( 30 0 ^{\circ} )}

What is the value of cos(100)cos(40)+sin(100)sin(40) ?
The value of cos(100)cos(40)+sin(100)sin(40) is 1/2