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}

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})

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

Use the following trivial identity:

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

Use the following trivial identity:

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