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

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

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

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

\frac{3}{3}

Decimal Notation

0.57735 \dots

Solution steps

\frac{sin ( \frac{π}{6} )}{cos ( \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}

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}

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

Simplify

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

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

Divide fractions:

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

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

Refine

= \frac{2}{2 3}

Cancel the common factor:

2

= \frac{1}{3}

Rationalize

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

\frac{1}{3}

Multiply by the conjugate

\frac{3}{3}

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

1 \cdot 3 = 3

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= \frac{3}{3}

= \frac{3}{3}

= \frac{3}{3}

cos (arccos (\frac{π}{2}))

tan (- 40 5^{\circ})

arccosh (3)

sin (4 5^{\circ}) sin (1 5^{\circ})

1 - 2 sin^{2} (\frac{5 π}{8})

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