What is the value of sin(72) ?

The value of sin(72) is (sqrt(2)sqrt(5+\sqrt{5)})/4

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sin(72)

sin (7 2^{\circ})

\frac{2 5 + 5}{4}

Solution steps

sin (7 2^{\circ})

Rewrite using trig identities:

cos (1 8^{\circ})

= cos (1 8^{\circ})

Rewrite using trig identities:

\frac{1 + cos ( 3 6 ^{\circ} )}{2}

= \frac{1 + cos ( 3 6 ^{\circ} )}{2}

Rewrite using trig identities:

cos (3 6^{\circ}) = \frac{5 + 1}{4}

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

Simplify

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

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

tan (- \frac{7 π}{12})

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

2 sin (π)

sin (7)

sin (2 3^{\circ})

What is the value of sin(72) ?
The value of sin(72) is (sqrt(2)sqrt(5+\sqrt{5)})/4