What is the value of (1-cos(150))/(sin(150)) ?

The value of (1-cos(150))/(sin(150)) is 2+sqrt(3)

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(1-cos(150))/(sin(150))

\frac{1 - cos ( 15 0 ^{\circ} )}{sin ( 15 0 ^{\circ} )}

2 + 3

Decimal Notation

3.73205 \dots

Solution steps

\frac{1 - cos ( 15 0 ^{\circ} )}{sin ( 15 0 ^{\circ} )}

Use the following trivial identity:

cos (15 0^{\circ}) = - \frac{3}{2}

cos (15 0^{\circ})

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= - \frac{3}{2}

Use the following trivial identity:

sin (15 0^{\circ}) = \frac{1}{2}

sin (15 0^{\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{1}{2}

= \frac{1 - ( - \frac{3}{2} )}{\frac{1}{2}}

Simplify

\frac{1 - ( - \frac{3}{2} )}{\frac{1}{2}} : 2 + 3

\frac{1 - ( - \frac{3}{2} )}{\frac{1}{2}}

Apply rule

- (- a) = a

= \frac{1 + \frac{3}{2}}{\frac{1}{2}}

Apply the fraction rule:

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

= \frac{( 1 + \frac{3}{2} ) \cdot 2}{1}

Join

1 + \frac{3}{2} : \frac{2 + 3}{2}

1 + \frac{3}{2}

Convert element to fraction:

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

= \frac{1 \cdot 2}{2} + \frac{3}{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 + 3}{2}

Multiply the numbers:

1 \cdot 2 = 2

= \frac{2 + 3}{2}

= \frac{2 \cdot \frac{2 + 3}{2}}{1}

Apply the fraction rule:

\frac{a}{1} = a

= \frac{2 + 3}{2} \cdot 2

Multiply fractions:

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

= \frac{( 2 + 3 ) \cdot 2}{2}

Cancel the common factor:

2

= 2 + 3

= 2 + 3

\frac{5}{tan ( 6 0 ^{\circ} )}

tan (\frac{4}{π})

arctan (\frac{41}{25})

\frac{2 cot ( 7 0 ^{\circ} ) ( 1 + sin ( 5 0 ^{\circ} ) )}{cos ( 1 0 ^{\circ} )}

cot (- 1 4^{\circ})

What is the value of (1-cos(150))/(sin(150)) ?
The value of (1-cos(150))/(sin(150)) is 2+sqrt(3)