What is the value of sin(345) ?

The value of sin(345) is (sqrt(2)-sqrt(6))/4

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sin(345)

sin (34 5^{\circ})

\frac{2 - 6}{4}

Solution steps

sin (34 5^{\circ})

Rewrite using trig identities:

sin (22 5^{\circ}) cos (12 0^{\circ}) + cos (22 5^{\circ}) sin (12 0^{\circ})

= sin (22 5^{\circ}) cos (12 0^{\circ}) + cos (22 5^{\circ}) sin (12 0^{\circ})

Rewrite using trig identities:

sin (22 5^{\circ}) = - \frac{2}{2}

Use the following trivial identity:

cos (12 0^{\circ}) = - \frac{1}{2}

Rewrite using trig identities:

cos (22 5^{\circ}) = - \frac{2}{2}

Use the following trivial identity:

sin (12 0^{\circ}) = \frac{3}{2}

= (- \frac{2}{2}) (- \frac{1}{2}) + (- \frac{2}{2}) \frac{3}{2}

Simplify

(- \frac{2}{2}) (- \frac{1}{2}) + (- \frac{2}{2}) \frac{3}{2} : \frac{2 - 6}{4}

= \frac{2 - 6}{4}

csc (18 0^{\circ})

cot (30 0^{\circ})

tan (- 6 0^{\circ})

sinh (2)

tan (- 3 0^{\circ})