What is the value of cot(-315) ?

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cot(-315)

cot (- 31 5^{\circ})

1

Solution steps

cot (- 31 5^{\circ})

Use the following property:

cot (- x) = - cot (x)

cot (- 31 5^{\circ}) = - cot (31 5^{\circ})

= - cot (31 5^{\circ})

cot (31 5^{\circ}) = cot (13 5^{\circ})

cot (31 5^{\circ})

Rewrite

31 5^{\circ}

18 0^{\circ} + 13 5^{\circ}

= cot (18 0^{\circ} + 13 5^{\circ})

Apply the periodicity of

cot

cot (x + 18 0^{\circ}) = cot (x)

cot (18 0^{\circ} + 13 5^{\circ}) = cot (13 5^{\circ})

= cot (13 5^{\circ})

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

Use the following trivial identity:

cot (13 5^{\circ}) = - 1

cot (13 5^{\circ})

cot (x)

periodicity table with

18 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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

= - 1

= - (- 1)

Simplify

= 1

cos (15 5^{\circ}) cos (3 5^{\circ}) + sin (15 5^{\circ}) sin (3 5^{\circ})

cos (24 0^{\circ} - 0^{\circ})

cot (66. 5^{\circ})

cos (10 1^{\circ})

sec (8 0^{\circ})