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

The value of (cos(pi/6))/(sin(pi/6)) is square root of 3

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(cos(pi/6))/(sin(pi/6))

\frac{cos ( \frac{π}{6} )}{sin ( \frac{π}{6} )}

3

Decimal Notation

1.73205 \dots

Solution steps

\frac{cos ( \frac{π}{6} )}{sin ( \frac{π}{6} )}

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

cos (\frac{π}{6})

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

Simplify

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

\frac{\frac{3}{2}}{\frac{1}{2}}

Divide fractions:

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

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

Refine

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

Cancel the common factor:

2

= 3

= 3

3 cos^{2} (\frac{7 π}{4})

arctan (0.26)

40 \cdot sec^{2} (\frac{\frac{20 π}{3}}{40}) \cdot \frac{1}{40} \cdot 355

3 (cos (\frac{π}{6}) + i sin (\frac{π}{6}))

arctan (0.07)

What is the value of (cos(pi/6))/(sin(pi/6)) ?
The value of (cos(pi/6))/(sin(pi/6)) is square root of 3