What is the limit as t approaches pi of cos(t/4) ?

The limit as t approaches pi of cos(t/4) is (sqrt(2))/2

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limit as t approaches pi of cos(t/4)

t \to π lim (cos (\frac{t}{4}))

\frac{2}{2}

Decimal

0.70710 \dots

Solution steps

t \to π lim (cos (\frac{t}{4}))

Plug in the value

t = π

= cos (\frac{π}{4})

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{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{2}{2}

y = x a^{2} - x^{2}

x - 2 sin (x)

y = x^{3}, y = 1, x = 2, x = 2

\int \frac{1}{3 x - 5} d x

x \to 0 - lim (\frac{3}{x} - \frac{3}{∣ x ∣})

What is the limit as t approaches pi of cos(t/4) ?
The limit as t approaches pi of cos(t/4) is (sqrt(2))/2