What is the value of arctan((0.5}{-\frac{sqrt(3))/2}) ?

The value of arctan((0.5}{-\frac{sqrt(3))/2}) is -pi/6

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arctan((0.5}{-\frac{sqrt(3))/2})

arctan (\frac{0.5}{- \frac{3}{2}})

- \frac{π}{6}

Solution steps

arctan (\frac{0.5}{- \frac{3}{2}})

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

Simplify:

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

= - \frac{π}{6}

arcsin (0.9975)

- 4 sin (2)

tan^{2} (4 5^{\circ} - 7.805)

\frac{2300}{tan ( 1 5 ^{\circ} )}

4 \cdot sin (\frac{1}{4})

What is the value of arctan((0.5}{-\frac{sqrt(3))/2}) ?
The value of arctan((0.5}{-\frac{sqrt(3))/2}) is -pi/6