What is the value of sin(153) ?

The value of sin(153) is (sqrt(2)sqrt(4-\sqrt{2)sqrt(5-\sqrt{5)}})/4

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sin(153)

sin (15 3^{\circ})

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

Solution steps

sin (15 3^{\circ})

Rewrite using trig identities:

sin (2 7^{\circ})

= 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}

arctan (\frac{6.3}{4.4})

cos (1 4^{\circ}) cos (8^{\circ}) + sin (1 4^{\circ}) sin (8^{\circ})

cos (\frac{5}{7})

cos (\frac{693 π}{4})

- 4 sin (\frac{4 π}{3})

What is the value of sin(153) ?
The value of sin(153) is (sqrt(2)sqrt(4-\sqrt{2)sqrt(5-\sqrt{5)}})/4