What is the limit as t approaches pi of sin(t/6) ?

The limit as t approaches pi of sin(t/6) is 1/2

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limit as t approaches pi of sin(t/6)

t \to π lim (sin (\frac{t}{6}))

\frac{1}{2}

Decimal

0.5

Solution steps

t \to π lim (sin (\frac{t}{6}))

Plug in the value

t = π

= sin (\frac{π}{6})

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

\frac{d y}{d x} = 2 y 16 - x^{2}, y (0) = 1

\frac{d}{d x} (ln (16 - x^{2}))

\int 2 (2 + x^{2})^{\frac{3}{2}} d x

\int x^{2} (x^{3} + 6)^{6} d x

f (x) = 1 + x^{3}, at x = 2

What is the limit as t approaches pi of sin(t/6) ?
The limit as t approaches pi of sin(t/6) is 1/2