What is the value of sin(99) ?

The value of sin(99) is (sqrt(2)sqrt(4+\sqrt{2)sqrt(5+\sqrt{5)}})/4

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sin(99)

sin (9 9^{\circ})

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

Solution steps

sin (9 9^{\circ})

Rewrite using trig identities:

\frac{1 - cos ( 19 8 ^{\circ} )}{2}

= \frac{1 - cos ( 19 8 ^{\circ} )}{2}

Rewrite using trig identities:

cos (19 8^{\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}

arctan (1000)

50 cos (4 5^{\circ})

sin (- \frac{7 π}{3})

tan (20 0^{\circ})

cos (- 2 0^{\circ})

What is the value of sin(99) ?
The value of sin(99) is (sqrt(2)sqrt(4+\sqrt{2)sqrt(5+\sqrt{5)}})/4