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Popular >

sqrt(3)tan(x)>1

Solution

3 tan (x) > 1

Solution

\frac{π}{6} + πn < x < \frac{π}{2} + πn

+2

Interval Notation

(\frac{π}{6} + πn, \frac{π}{2} + πn)

Decimal Notation

0.52359 \dots + πn < x < 1.57079 \dots + πn

Solution steps

3 tan (x) > 1

Divide both sides by

3

3 tan (x) > 1

Divide both sides by

3

\frac{3 tan ( x )}{3} > \frac{1}{3}

Simplify

\frac{3 tan ( x )}{3} > \frac{1}{3}

Simplify

\frac{3 tan ( x )}{3} : tan (x)

\frac{3 tan ( x )}{3}

Cancel the common factor:

3

= tan (x)

Simplify

\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}

tan (x) > \frac{3}{3}

tan (x) > \frac{3}{3}

tan (x) > \frac{3}{3}

If

tan (x) > a

then

arctan (a) + πn < x < \frac{π}{2} + πn

arctan (\frac{3}{3}) + πn < x < \frac{π}{2} + πn

Simplify

arctan (\frac{3}{3}) : \frac{π}{6}

arctan (\frac{3}{3})

Use the following trivial identity:

arctan (\frac{3}{3}) = \frac{π}{6}

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} + πn < x < \frac{π}{2} + πn

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