What is the value of arctan((1/2}{-\frac{sqrt(3))/2}) ?

The value of arctan((1/2}{-\frac{sqrt(3))/2}) is -pi/6

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arctan((1/2}{-\frac{sqrt(3))/2})

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

- \frac{π}{6}

Decimal Notation

- 30

Solution steps

arctan (\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}}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \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}

= arctan (- \frac{3}{3})

Use the following property:

arctan (- x) = - arctan (x)

arctan (- \frac{3}{3}) = - arctan (\frac{3}{3})

= - arctan (\frac{3}{3})

Use the following trivial identity:

arctan (\frac{3}{3}) = \frac{π}{6}

arctan (\frac{3}{3})

x 0 \frac{3}{3} 13 arctan (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} arctan (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ}

= \frac{π}{6}

= - \frac{π}{6}

sin (3 (\frac{π}{2}))

sin (2 \cdot 60)

arcsin (\frac{1}{1.6})

2 \cdot cos (\frac{π}{3})

2 \cdot cos (\frac{π}{4})

What is the value of arctan((1/2}{-\frac{sqrt(3))/2}) ?
The value of arctan((1/2}{-\frac{sqrt(3))/2}) is -pi/6