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Popular >

6cos(x)+4>0,0<= x<2pi

Solution

6 cos (x) + 4 > 0, 0 \leq x < 2 π

Solution

0 \leq x < arccos (- \frac{2}{3}) or 2 π - arccos (- \frac{2}{3}) < x < 2 π

+2

Interval Notation

Decimal

0 \leq x < 2.30052 \dots or 3.98266 \dots < x < 6.28318 \dots

Solution steps

6 cos (x) + 4 > 0, 0 \leq x < 2 π

Move

4

to the right side

6 cos (x) + 4 > 0

Subtract

4

from both sides

6 cos (x) + 4 - 4 > 0 - 4

Simplify

6 cos (x) > - 4

6 cos (x) > - 4

Divide both sides by

6

6 cos (x) > - 4

Divide both sides by

6

\frac{6 cos ( x )}{6} > \frac{- 4}{6}

Simplify

\frac{6 cos ( x )}{6} > \frac{- 4}{6}

Simplify

\frac{6 cos ( x )}{6} : cos (x)

\frac{6 cos ( x )}{6}

Divide the numbers:

\frac{6}{6} = 1

= cos (x)

Simplify

\frac{- 4}{6} : - \frac{2}{3}

\frac{- 4}{6}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{4}{6}

Cancel the common factor:

2

= - \frac{2}{3}

cos (x) > - \frac{2}{3}

cos (x) > - \frac{2}{3}

cos (x) > - \frac{2}{3}

For

cos (x) > a

, if

- 1 \leq a < 1

then

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

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

Combine the intervals

- arccos (- \frac{2}{3}) + 2 πn < x < arccos (- \frac{2}{3}) + 2 πn and 0 \leq x < 2 π

0 \leq x < arccos (- \frac{2}{3}) or 2 π - arccos (- \frac{2}{3}) < x < 2 π

Graph

Popular Examples

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