What is the value of (cos(5pi))/6 ?

The value of (cos(5pi))/6 is -1/6

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(cos(5pi))/6

\frac{cos ( 5 π )}{6}

- \frac{1}{6}

Decimal Notation

- 0.16666 \dots

Solution steps

\frac{cos ( 5 π )}{6}

Rewrite using trig identities:

cos (5 π) = - 1

cos (5 π)

cos (5 π) = cos (π)

cos (5 π)

Rewrite

5 π

2 π \cdot 2 + π

= cos (2 π 2 + π)

Apply the periodicity of

cos

cos (x + 2 π \cdot k) = cos (x)

cos (2 π \cdot 2 + 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}{6}

Simplify

= - \frac{1}{6}

arctan (cos (\frac{π}{2}))

sin (arctan (3))

cos (11 0^{\circ}) cos (2 0^{\circ}) - sin (11 0^{\circ}) sin (2 0^{\circ})

sec (40 5^{\circ})

\frac{8.8}{sin ( 3 3 ^{\circ} )}