What is the value of 1/(1-sin(pi/6)) ?

The value of 1/(1-sin(pi/6)) is 2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

1/(1-sin(pi/6))

\frac{1}{1 - sin ( \frac{π}{6} )}

2

Solution steps

\frac{1}{1 - sin ( \frac{π}{6} )}

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

sin (\frac{π}{6})

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

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

Simplify

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

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

Join

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

1 - \frac{1}{2}

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

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

1 \cdot 2 - 1 = 1

1 \cdot 2 - 1

Multiply the numbers:

1 \cdot 2 = 2

= 2 - 1

Subtract the numbers:

2 - 1 = 1

= 1

= \frac{1}{2}

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

Apply the fraction rule:

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

= \frac{2}{1}

Apply rule

\frac{a}{1} = a

= 2

= 2

cot (arcsin (\frac{1}{4}))

\frac{sin ( 24 0 ^{\circ} )}{cos ( 12 0 ^{\circ} )}

5 + 4 cos (\frac{π}{2})

(sin (3 0^{\circ})) (tan (4 5^{\circ})) + (tan (3 0^{\circ})) (sin (6 0^{\circ}))

cos (arctan (\frac{5}{12}) + arcsin (\frac{4}{5}))