What is the value of sin(1380) ?

The value of sin(1380) is -(sqrt(3))/2

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sin(1380)

sin (138 0^{\circ})

- \frac{3}{2}

Solution steps

sin (138 0^{\circ})

sin (138 0^{\circ}) = sin (30 0^{\circ})

= sin (30 0^{\circ})

Rewrite using trig identities:

sin (18 0^{\circ}) cos (12 0^{\circ}) + cos (18 0^{\circ}) sin (12 0^{\circ})

= sin (18 0^{\circ}) cos (12 0^{\circ}) + cos (18 0^{\circ}) sin (12 0^{\circ})

Use the following trivial identity:

sin (18 0^{\circ}) = 0

Use the following trivial identity:

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

Use the following trivial identity:

cos (18 0^{\circ}) = (- 1)

Use the following trivial identity:

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

= 0 \cdot (- \frac{1}{2}) + (- 1) \frac{3}{2}

Simplify

= - \frac{3}{2}

sin^{7} (9 0^{\circ})

sech (- 2)

cot (arcsin (\frac{7}{9}))

4 sin (2 \cdot \frac{π}{6})

cos (π (- 1))