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

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

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

t \to π lim (cos (\frac{2 t}{3}))

- \frac{1}{2}

Decimal

- 0.5

Solution steps

t \to π lim (cos (\frac{2 t}{3}))

Plug in the value

t = π

= cos (\frac{2 π}{3})

Use the following trivial identity:

cos (\frac{2 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}

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