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

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

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sin(1/3 pi)*1

sin (\frac{1}{3} π) \cdot 1

\frac{3}{2}

Decimal Notation

0.86602 \dots

Solution steps

sin (\frac{1}{3} π) \cdot 1

Rewrite using trig identities:

sin (\frac{1}{3} π) = \frac{3}{2}

sin (\frac{1}{3} π)

Simplify:

\frac{1}{3} π = \frac{π}{3}

\frac{1}{3} π

Multiply fractions:

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

= \frac{1 π}{3}

Multiply:

1 π = π

= \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} \cdot 1

Simplify

= \frac{3}{2}

(cos (26. 8^{\circ}) (39.6)) \cdot 1.27

3 sin (6 5^{\circ}) - 65 cos (6 5^{\circ})

2 sin (3 0^{\circ}) cos (6 0^{\circ})

(cos (6 0^{\circ}) + sin (4 5^{\circ})) cos (3 0^{\circ})

tan (38.6 6^{\circ})