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

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

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

x \to \frac{π}{6} lim (cos (x))

\frac{3}{2}

Decimal Notation

0.86602 \dots

Solution steps

x \to \frac{π}{6} lim (cos (x))

Plug in the value

x = \frac{π}{6}

= 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}

x \to - 2 lim (\frac{5}{( x + 2 ) ^{2}})

x \to 2 lim (3 x^{2} - 5 x - 2)

x \to - \infty lim (x \cdot 1)

x \to 3 lim (19 x - 4)

x \to - 4 - lim (\frac{1}{16 - x ^{2}})

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