What is the value of sin(2(pi/6))-pi/6 ?

The value of sin(2(pi/6))-pi/6 is (sqrt(3))/2-pi/6

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sin(2(pi/6))-pi/6

sin (2 (\frac{π}{6})) - \frac{π}{6}

\frac{3}{2} - \frac{π}{6}

Decimal Notation

0.34242 \dots

Solution steps

sin (2 (\frac{π}{6})) - \frac{π}{6}

= sin (2 \cdot \frac{π}{6}) - \frac{π}{6}

Rewrite using trig identities:

sin (2 \cdot \frac{π}{6}) = \frac{3}{2}

sin (2 \cdot \frac{π}{6})

Simplify:

2 \cdot \frac{π}{6} = \frac{π}{3}

2 \cdot \frac{π}{6}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{π 2}{6}

Cancel the common factor:

2

= \frac{π}{3}

= sin (\frac{π}{3})

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

sin (\frac{π}{3})

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{3}{2}

= \frac{3}{2}

= \frac{3}{2} - \frac{π}{6}

\frac{π}{2} \cdot cos (\frac{π}{2})

arctan (\frac{8}{5})

sin (\frac{- 2}{2})

arctan (\frac{50}{70})

arcsec (1.4)

What is the value of sin(2(pi/6))-pi/6 ?
The value of sin(2(pi/6))-pi/6 is (sqrt(3))/2-pi/6