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

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

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sin(pi-pi/3)

sin (π - \frac{π}{3})

\frac{3}{2}

Decimal Notation

0.86602 \dots

Solution steps

sin (π - \frac{π}{3})

Simplify:

π - \frac{π}{3} = \frac{2 π}{3}

π - \frac{π}{3}

Convert element to fraction:

π = \frac{π 3}{3}

= \frac{π 3}{3} - \frac{π}{3}

Since the denominators are equal, combine the fractions:

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

= \frac{π 3 - π}{3}

Add similar elements:

3 π - π = 2 π

= \frac{2 π}{3}

= 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}

= \frac{3}{2}

sin (2) \cdot sin (3)

\frac{1 0 ^{4} \cdot 1.6 \cdot 0.6}{41} \cdot sin (9 0^{\circ} + arctan (\frac{4}{5}))

arccos (0.974631846)

3 cos (2 (π))

450 \cdot cos (3 0^{\circ})