What is the value of sin(1314) ?

The value of sin(1314) is -(sqrt(5)+1)/4

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sin(1314)

sin (131 4^{\circ})

- \frac{5 + 1}{4}

Solution steps

sin (131 4^{\circ})

sin (131 4^{\circ}) = sin (23 4^{\circ})

= sin (23 4^{\circ})

Rewrite using trig identities:

cos (14 4^{\circ})

= cos (14 4^{\circ})

Rewrite using trig identities:

- cos (3 6^{\circ})

= - cos (3 6^{\circ})

Rewrite using trig identities:

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

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

- 5 sin (\frac{2 π}{3})

8 sin (\frac{π}{4}) sin (\frac{π}{6})

arctan (- \frac{5}{11})

sin^{2} (6 0^{\circ}) - cos^{2} (6 0^{\circ})

5 cos (\frac{4 π}{3})