What is the value of csc(-405) ?

The value of csc(-405) is -sqrt(2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

csc(-405)

csc (- 40 5^{\circ})

- 2

Decimal Notation

- 1.41421 \dots

Solution steps

csc (- 40 5^{\circ})

Use the following property:

csc (- x) = - csc (x)

csc (- 40 5^{\circ}) = - csc (40 5^{\circ})

= - csc (40 5^{\circ})

csc (40 5^{\circ}) = csc (4 5^{\circ})

csc (40 5^{\circ})

Rewrite

40 5^{\circ}

36 0^{\circ} + 4 5^{\circ}

= csc (36 0^{\circ} + 4 5^{\circ})

Apply the periodicity of

csc

csc (x + 36 0^{\circ}) = csc (x)

csc (36 0^{\circ} + 4 5^{\circ}) = csc (4 5^{\circ})

= csc (4 5^{\circ})

= - csc (4 5^{\circ})

Use the following trivial identity:

csc (4 5^{\circ}) = 2

csc (4 5^{\circ})

csc (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} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 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} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

= 2

= - 2

cot (\frac{31 π}{6})

tan (43 5^{\circ}) + tan (37 5^{\circ})

sin^{2} (\frac{π}{4}) + cos^{2} (\frac{π}{4})

cos (- 7 π)

25 cos (6 0^{\circ})