What is the value of cos(18)sin(-72) ?

The value of cos(18)sin(-72) is (-5-sqrt(5))/8

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cos(18)sin(-72)

cos (1 8^{\circ}) sin (- 7 2^{\circ})

\frac{- 5 - 5}{8}

Solution steps

cos (1 8^{\circ}) sin (- 7 2^{\circ})

Rewrite using trig identities:

\frac{- sin ( 5 4 ^{\circ} ) - sin ( 9 0 ^{\circ} )}{2}

= \frac{- sin ( 5 4 ^{\circ} ) - sin ( 9 0 ^{\circ} )}{2}

Rewrite using trig identities:

sin (5 4^{\circ}) = \frac{5 + 1}{4}

Use the following trivial identity:

sin (9 0^{\circ}) = 1

= \frac{- \frac{5 + 1}{4} - 1}{2}

Simplify

\frac{- \frac{5 + 1}{4} - 1}{2} : \frac{- 5 - 5}{8}

= \frac{- 5 - 5}{8}

arccos (\frac{5}{10})

sin (\frac{3 π}{10}) - sin (\frac{π}{10})

sin (\frac{6}{8})

arccos (7)

3 sin (\frac{5 π}{6})

What is the value of cos(18)sin(-72) ?
The value of cos(18)sin(-72) is (-5-sqrt(5))/8