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Popular >

-3cos(x)+1>=-1

Solution

- 3 cos (x) + 1 \geq - 1

Solution

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

+2

Interval Notation

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

Decimal Notation

0.84106 \dots + 2 πn \leq x \leq 5.44211 \dots + 2 πn

Solution steps

- 3 cos (x) + 1 \geq - 1

Move

1

to the right side

- 3 cos (x) + 1 \geq - 1

Subtract

1

from both sides

- 3 cos (x) + 1 - 1 \geq - 1 - 1

Simplify

- 3 cos (x) \geq - 2

- 3 cos (x) \geq - 2

Multiply both sides by

- 1

- 3 cos (x) \geq - 2

Multiply both sides by -1 (reverse the inequality)

(- 3 cos (x)) (- 1) \leq (- 2) (- 1)

Simplify

3 cos (x) \leq 2

3 cos (x) \leq 2

Divide both sides by

3

3 cos (x) \leq 2

Divide both sides by

3

\frac{3 cos ( x )}{3} \leq \frac{2}{3}

Simplify

cos (x) \leq \frac{2}{3}

cos (x) \leq \frac{2}{3}

For

cos (x) \leq a

, if

- 1 < a < 1

then

arccos (a) + 2 πn \leq x \leq 2 π - arccos (a) + 2 πn

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

Popular Examples

2cos^2(x)-3cos(x)+1<0

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cos^2(x)>= cos(x)

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sqrt(3)cot(x/2)>-3

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

tan(θ)>0,cos(θ)<0sin(θ)=-2/5 ,tan(θ)

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