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Popular >

sqrt(3)cos(x)-1<0

Solution

3 cos (x) - 1 < 0

Solution

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

+2

Interval Notation

(arccos (\frac{3}{3}) + 2 πn, 2 π - arccos (\frac{3}{3}) + 2 πn)

Decimal Notation

0.95531 \dots + 2 πn < x < 5.32786 \dots + 2 πn

Solution steps

3 cos (x) - 1 < 0

Move

1

to the right side

3 cos (x) - 1 < 0

Add

1

to both sides

3 cos (x) - 1 + 1 < 0 + 1

Simplify

3 cos (x) < 1

3 cos (x) < 1

Divide both sides by

3

3 cos (x) < 1

Divide both sides by

3

\frac{3 cos ( x )}{3} < \frac{1}{3}

Simplify

\frac{3 cos ( x )}{3} < \frac{1}{3}

Simplify

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

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

Cancel the common factor:

3

= cos (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}

cos (x) < \frac{3}{3}

cos (x) < \frac{3}{3}

cos (x) < \frac{3}{3}

For

cos (x) < a

, if

- 1 < a \leq 1

then

arccos (a) + 2 πn < x < 2 π - arccos (a) + 2 πn

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

Popular Examples

tan(x)>-sqrt(3)

tan (x) > - 3

(9sin(t)+1)/8 <= 2pi

\frac{9 sin ( t ) + 1}{8} \leq 2 π

(2cos(θ)+1)/(2sin(θ)-sqrt(3))>0

\frac{2 cos ( θ ) + 1}{2 sin ( θ ) - 3} > 0

- 1 - cos (t) \geq 0

cos (π x) < - \frac{1}{2}