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

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

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limit as t approaches pi of cos(t/3)

t \to π lim (cos (\frac{t}{3}))

\frac{1}{2}

Decimal

0.5

Solution steps

t \to π lim (cos (\frac{t}{3}))

Plug in the value

t = π

= 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}

\int_{0}^{\infty} e^{- 7 x} d x

f (x) = 2 x + \frac{x ^{2} - x}{x ^{3} + x + 1}

\frac{d}{d x} (e^{- x^{2} - 5 x})

\frac{d}{d x} (\frac{e ^{2 x}}{x ^{2}})

\int x^{2} - 7 x + 6 d x

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