What is the value of sin(27) ?

The value of sin(27) is (sqrt(2)sqrt(4-\sqrt{2)sqrt(5-\sqrt{5)}})/4

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sin(27)

sin (2 7^{\circ})

\frac{2 4 - 2 5 - 5}{4}

Solution steps

sin (2 7^{\circ})

Rewrite using trig identities:

\frac{1 - cos ( 5 4 ^{\circ} )}{2}

= \frac{1 - cos ( 5 4 ^{\circ} )}{2}

Rewrite using trig identities:

cos (5 4^{\circ}) = \frac{2 5 - 5}{4}

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

Simplify

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

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

sin (3 1^{\circ})

arcsin (sin (\frac{7 π}{3}))

cos (- \frac{5 π}{12})

arctan (- \frac{3}{2})

arcsec (0)

What is the value of sin(27) ?
The value of sin(27) is (sqrt(2)sqrt(4-\sqrt{2)sqrt(5-\sqrt{5)}})/4