What is the limit as x approaches 0 of sin(pi/6) ?

The limit as x approaches 0 of sin(pi/6) is 1/2

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limit as x approaches 0 of sin(pi/6)

x \to 0 lim (sin (\frac{π}{6}))

\frac{1}{2}

Decimal Notation

0.5

Solution steps

x \to 0 lim (sin (\frac{π}{6}))

x \to a lim c = c

= 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}

x \to 0 lim (e^{- \frac{1}{x ^{4}}})

x \to 3 lim (2 x^{2} + 3)

x \to 1 lim (x^{2} + 2 x - 1)

x \to 3 lim (2 x 12 - x)

x \to 3 lim (7 x)

What is the limit as x approaches 0 of sin(pi/6) ?
The limit as x approaches 0 of sin(pi/6) is 1/2