What is the value of (sin(240))/5 ?

The value of (sin(240))/5 is -(sqrt(3))/(10)

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(sin(240))/5

\frac{sin ( 24 0 ^{\circ} )}{5}

- \frac{3}{10}

Decimal Notation

- 0.17320 \dots

Solution steps

\frac{sin ( 24 0 ^{\circ} )}{5}

Rewrite using trig identities:

sin (24 0^{\circ}) = 2 sin (12 0^{\circ}) cos (12 0^{\circ})

sin (24 0^{\circ})

Write

sin (24 0^{\circ})

sin (2 \cdot 12 0^{\circ})

= sin (2 \cdot 12 0^{\circ})

Use the Double Angle identity:

sin (2 x) = 2 sin (x) cos (x)

= 2 sin (12 0^{\circ}) cos (12 0^{\circ})

= \frac{2 sin ( 12 0 ^{\circ} ) cos ( 12 0 ^{\circ} )}{5}

Use the following trivial identity:

sin (12 0^{\circ}) = \frac{3}{2}

sin (12 0^{\circ})

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} 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}

Use the following trivial identity:

cos (12 0^{\circ}) = - \frac{1}{2}

cos (12 0^{\circ})

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= - \frac{1}{2}

= \frac{2 \cdot \frac{3}{2} ( - \frac{1}{2} )}{5}

Simplify

\frac{2 \cdot \frac{3}{2} ( - \frac{1}{2} )}{5} : - \frac{3}{10}

\frac{2 \cdot \frac{3}{2} ( - \frac{1}{2} )}{5}

Remove parentheses:

(- a) = - a

= \frac{- 2 \cdot \frac{3}{2} \cdot \frac{1}{2}}{5}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{2 \cdot \frac{3}{2} \cdot \frac{1}{2}}{5}

Multiply

2 \cdot \frac{3}{2} \cdot \frac{1}{2} : \frac{3}{2}

2 \cdot \frac{3}{2} \cdot \frac{1}{2}

Multiply fractions:

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

= \frac{3 \cdot 1 \cdot 2}{2 \cdot 2}

Cancel the common factor:

2

= \frac{3 \cdot 1}{2}

Multiply:

3 \cdot 1 = 3

= \frac{3}{2}

= - \frac{\frac{3}{2}}{5}

Simplify

\frac{\frac{3}{2}}{5} : \frac{3}{10}

\frac{\frac{3}{2}}{5}

Apply the fraction rule:

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

= \frac{3}{2 \cdot 5}

Multiply the numbers:

2 \cdot 5 = 10

= \frac{3}{10}

= - \frac{3}{10}

= - \frac{3}{10}

\frac{cos ( \frac{π}{6} )}{cos ( \frac{7 π}{4} )}

2 cos (- 12 0^{\circ})

sin (36. 5^{\circ})

cos (\frac{π}{3}) - sin (\frac{3 π}{4})

arctan (\frac{16}{8})

What is the value of (sin(240))/5 ?
The value of (sin(240))/5 is -(sqrt(3))/(10)