What is the value of (cos(7pi))/(12) ?

The value of (cos(7pi))/(12) is -1/12

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(cos(7pi))/(12)

\frac{cos ( 7 π )}{12}

- \frac{1}{12}

Decimal Notation

- 0.08333 \dots

Solution steps

\frac{cos ( 7 π )}{12}

Rewrite using trig identities:

cos (7 π) = - 1

cos (7 π)

cos (7 π) = cos (π)

cos (7 π)

Rewrite

7 π

2 π \cdot 3 + π

= cos (2 π 3 + π)

Apply the periodicity of

cos

cos (x + 2 π \cdot k) = cos (x)

cos (2 π \cdot 3 + π) = cos (π)

= cos (π)

= cos (π)

Use the following trivial identity:

cos (π) = (- 1)

cos (π)

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}

= (- 1)

= - 1

= \frac{- 1}{12}

Simplify

= - \frac{1}{12}

sin (\frac{21}{29})

tan (\frac{5 π}{6} - \frac{π}{4})

tan (arcsin (\frac{3}{5}) + arccos (1))

sin (\frac{3 π}{\frac{2}{2}})

cos (arcsin (\frac{5}{13}) + arctan (\frac{3}{4}))