What is the general solution for -pi/6 =arctan(x) ?

The general solution for -pi/6 =arctan(x) is x=-(sqrt(3))/3

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-pi/6 =arctan(x)

- \frac{π}{6} = arctan (x)

x = - \frac{3}{3}

Solution steps

- \frac{π}{6} = arctan (x)

Switch sides

arctan (x) = - \frac{π}{6}

Apply trig inverse properties

arctan (x) = - \frac{π}{6}

arctan (x) = a \Rightarrow x = tan (a)

x = tan (- \frac{π}{6})

tan (- \frac{π}{6}) = - \frac{3}{3}

tan (- \frac{π}{6})

Use the following property:

tan (- x) = - tan (x)

tan (- \frac{π}{6}) = - tan (\frac{π}{6})

= - tan (\frac{π}{6})

Use the following trivial identity:

tan (\frac{π}{6}) = \frac{3}{3}

tan (\frac{π}{6})

tan (x)

periodicity table with

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= \frac{3}{3}

= - \frac{3}{3}

x = - \frac{3}{3}

x = - \frac{3}{3}

sin^{2} (x) - sin (x) cos (x) = 0

cot (χ - \frac{π}{4}) = - 1

cos (3 x - 1) = 0

x, sec^{2} (x y) y = 0

tan (x + 7) = cot (4 x + 8)

What is the general solution for -pi/6 =arctan(x) ?
The general solution for -pi/6 =arctan(x) is x=-(sqrt(3))/3