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

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

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

t \to \frac{π}{4} lim (\frac{sin ( t )}{t})

\frac{2 2}{π}

Decimal Notation

0.90031 \dots

Solution steps

t \to \frac{π}{4} lim (\frac{sin ( t )}{t})

Plug in the value

t = \frac{π}{4}

= \frac{sin ( \frac{π}{4} )}{\frac{π}{4}}

Simplify

\frac{sin ( \frac{π}{4} )}{\frac{π}{4}} : \frac{2 2}{π}

= \frac{2 2}{π}

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