What is the limit as x approaches 1 of cos(pi/3) ?

The limit as x approaches 1 of cos(pi/3) is 1/2

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limit as x approaches 1 of cos(pi/3)

x \to 1 lim (cos (\frac{π}{3}))

\frac{1}{2}

Decimal Notation

0.5

Solution steps

x \to 1 lim (cos (\frac{π}{3}))

x \to a lim c = c

= cos (\frac{π}{3})

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{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{1}{2}

\frac{d}{d x} (\frac{2}{3} π + 1)

\frac{\partial}{\partial x} (\frac{( 2 x + y )}{z})

\int cos (4 x) cos (5 x) d x

x^{2} + 6 x - 3

49 y^{^{''}} + 42 y^{^{'}} + 9 y = 0, y (0) = a, y^{^{'}} (0) = 2

What is the limit as x approaches 1 of cos(pi/3) ?
The limit as x approaches 1 of cos(pi/3) is 1/2