What is the value of csc(-135) ?

The value of csc(-135) is -sqrt(2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

csc(-135)

csc (- 13 5^{\circ})

- 2

Decimal Notation

- 1.41421 \dots

Solution steps

csc (- 13 5^{\circ})

Use the following property:

csc (- x) = - csc (x)

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

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

Rewrite using trig identities:

csc (13 5^{\circ}) = 2

csc (13 5^{\circ})

Rewrite using trig identities:

\frac{1}{sin ( 13 5 ^{\circ} )}

csc (13 5^{\circ})

Use the basic trigonometric identity:

csc (x) = \frac{1}{sin ( x )}

= \frac{1}{sin ( 13 5 ^{\circ} )}

= \frac{1}{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{1}{\frac{2}{2}}

Simplify

\frac{1}{\frac{2}{2}} : 2

\frac{1}{\frac{2}{2}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{2}{2}

Apply radical rule:

2 = 2^{\frac{1}{2}}

= \frac{2}{2 ^{\frac{1}{2}}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{2 ^{1}}{2 ^{\frac{1}{2}}} = 2^{1 - \frac{1}{2}}

= 2^{1 - \frac{1}{2}}

Subtract the numbers:

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

= 2^{\frac{1}{2}}

Apply radical rule:

2^{\frac{1}{2}} = 2

= 2

= 2

= - 2

cos (10 5^{\circ}) + cos (1 5^{\circ})

arctan (0.35)

5 sin (0)

cos (\frac{21 π}{4})

\frac{1}{cos ( 3 0 ^{\circ} )}