What is the value of 1-sin((2pi)/3) ?

The value of 1-sin((2pi)/3) is 1-(sqrt(3))/2

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1-sin((2pi)/3)

1 - sin (\frac{2 π}{3})

1 - \frac{3}{2}

Decimal Notation

0.13397 \dots

Solution steps

1 - sin (\frac{2 π}{3})

Use the following trivial identity:

sin (\frac{2 π}{3}) = \frac{3}{2}

sin (\frac{2 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}

= 1 - \frac{3}{2}

20 cos (5 0^{\circ})

\frac{9}{cos ( 3 0 ^{\circ} )}

2 sec (- \frac{π}{4})

5 \cdot sin (3 5^{\circ})

arctan (\frac{20}{21})

What is the value of 1-sin((2pi)/3) ?
The value of 1-sin((2pi)/3) is 1-(sqrt(3))/2