What is the value of sin(375) ?

The value of sin(375) is (sqrt(6)-sqrt(2))/4

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sin(375)

sin (37 5^{\circ})

\frac{6 - 2}{4}

Solution steps

sin (37 5^{\circ})

sin (37 5^{\circ}) = sin (1 5^{\circ})

= sin (1 5^{\circ})

Rewrite using trig identities:

sin (4 5^{\circ}) cos (3 0^{\circ}) - cos (4 5^{\circ}) sin (3 0^{\circ})

= sin (4 5^{\circ}) cos (3 0^{\circ}) - cos (4 5^{\circ}) sin (3 0^{\circ})

Use the following trivial identity:

sin (4 5^{\circ}) = \frac{2}{2}

Use the following trivial identity:

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

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

= \frac{2}{2} \cdot \frac{3}{2} - \frac{2}{2} \cdot \frac{1}{2}

Simplify

\frac{2}{2} \cdot \frac{3}{2} - \frac{2}{2} \cdot \frac{1}{2} : \frac{6 - 2}{4}

= \frac{6 - 2}{4}

cos (\frac{5}{12})

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

- 5 sin (π)

arctan (\frac{20}{15})

2 (cos (\frac{2 π}{3}) + i sin (\frac{2 π}{3}))