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Popular >

sqrt(3)-tan(x)<0

Solution

3 - tan (x) < 0

Solution

\frac{π}{3} + πn < x < \frac{π}{2} + πn

+2

Interval Notation

(\frac{π}{3} + πn, \frac{π}{2} + πn)

Decimal Notation

1.04719 \dots + πn < x < 1.57079 \dots + πn

Solution steps

3 - tan (x) < 0

Move

3

to the right side

3 - tan (x) < 0

Subtract

3

from both sides

3 - tan (x) - 3 < 0 - 3

Simplify

- tan (x) < - 3

- tan (x) < - 3

Multiply both sides by

- 1

- tan (x) < - 3

Multiply both sides by -1 (reverse the inequality)

(- tan (x)) (- 1) > (- 3) (- 1)

Simplify

tan (x) > 3

tan (x) > 3

If

tan (x) > a

then

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

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

Simplify

arctan (3) : \frac{π}{3}

arctan (3)

Use the following trivial identity:

arctan (3) = \frac{π}{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}{3}

\frac{π}{3} + πn < x < \frac{π}{2} + πn

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