What is the value of sin(-855) ?

The value of sin(-855) is -(sqrt(2))/2

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sin(-855)

sin (- 85 5^{\circ})

- \frac{2}{2}

Solution steps

sin (- 85 5^{\circ})

Use the following property:

sin (- x) = - sin (x)

sin (- 85 5^{\circ}) = - sin (85 5^{\circ})

= - sin (85 5^{\circ})

sin (85 5^{\circ}) = sin (13 5^{\circ})

= - sin (13 5^{\circ})

Use the following trivial identity:

sin (13 5^{\circ}) = \frac{2}{2}

= - \frac{2}{2}

cos (24 5^{\circ})

csc^{2} (3 0^{\circ}) + tan^{2} (4 5^{\circ})

tan (\frac{π}{4}) - tan (- \frac{π}{4})

2^{\frac{1}{4}} [cos (\frac{1}{8} π) + i sin (\frac{1}{8} π)]

arccos (tan (- \frac{5 π}{4}))