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

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

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sin(pi/3+pi/3)

sin (\frac{π}{3} + \frac{π}{3})

\frac{3}{2}

Decimal Notation

0.86602 \dots

Solution steps

sin (\frac{π}{3} + \frac{π}{3})

Simplify:

\frac{π}{3} + \frac{π}{3} = \frac{2 π}{3}

\frac{π}{3} + \frac{π}{3}

Apply rule

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

= \frac{π + π}{3}

Add similar elements:

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}

arctan (\frac{15}{4})

4 sin (2) (\frac{π}{6})

arccos (\frac{2}{3 38})

- csc^{2} (9 0^{\circ})

0.3 \cdot sin (3 0^{\circ})

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