What is the value of pi/3-sin(pi/3) ?

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

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pi/3-sin(pi/3)

\frac{π}{3} - sin (\frac{π}{3})

\frac{π}{3} - \frac{3}{2}

Decimal Notation

0.18117 \dots

Solution steps

\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{π}{3} - \frac{3}{2}

cos (187. 5^{\circ})

1 + cos (12 0^{\circ})

2 - 2 cosh (1)

\frac{cot ^{2} ( 3 5 ^{\circ} )}{cot ^{2} ( 2 5 ^{\circ} )}

\frac{52}{cos ( 3 7 ^{\circ} )}

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