What is the value of sin(-855) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(-855)

sin (- 85 5^{\circ})

- \frac{2}{2}

Decimal Notation

- 0.70710 \dots

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 (85 5^{\circ})

Rewrite

85 5^{\circ}

36 0^{\circ} \cdot 2 + 13 5^{\circ}

= sin (36 0^{\circ} 2 + 13 5^{\circ})

Apply the periodicity of

sin

sin (x + 36 0^{\circ} \cdot k) = sin (x)

sin (36 0^{\circ} \cdot 2 + 13 5^{\circ}) = sin (13 5^{\circ})

= sin (13 5^{\circ})

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

Use the following trivial identity:

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

sin (13 5^{\circ})

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \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}))