What is the limit as x approaches pi of cos(x/6) ?

The limit as x approaches pi of cos(x/6) is (sqrt(3))/2

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limit as x approaches pi of cos(x/6)

x \to π lim (cos (\frac{x}{6}))

\frac{3}{2}

Decimal Notation

0.86602 \dots

Solution steps

x \to π lim (cos (\frac{x}{6}))

Plug in the value

x = π

= cos (\frac{π}{6})

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

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{3}{2}

f (x) = - \frac{1}{4} x^{4} + \frac{27}{2} x^{2}

\int \frac{m ^{2}}{m + 1} d m

\frac{64 x}{x ^{2} + 64}

\int x^{2} ln (x) d x

\frac{d}{d x} (x^{4} - 5 x^{3})

What is the limit as x approaches pi of cos(x/6) ?
The limit as x approaches pi of cos(x/6) is (sqrt(3))/2