English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

6.5*sin(5x)>= 5.6

Solution

6.5 \cdot sin (5 x) \geq 5.6

Solution

\frac{arcsin ( \frac{56}{65} )}{5} + \frac{2 π}{5} n \leq x \leq \frac{π - arcsin ( \frac{56}{65} )}{5} + \frac{2 π}{5} n

Interval Notation

[\frac{arcsin ( \frac{56}{65} )}{5} + \frac{2 π}{5} n, \frac{π - arcsin ( \frac{56}{65} )}{5} + \frac{2 π}{5} n]

Decimal Notation

0.20765 \dots + \frac{2 π}{5} n \leq x \leq 0.42066 \dots + \frac{2 π}{5} n

Solution steps

6.5 sin (5 x) \geq 5.6

Multiply both sides by

10

6.5 sin (5 x) \geq 5.6

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere is one digit to the right of the decimal point, therefore multiply by

10

6.5 sin (5 x) \cdot 10 \geq 5.6 \cdot 10

Refine

65 sin (5 x) \geq 56

65 sin (5 x) \geq 56

Divide both sides by

65

65 sin (5 x) \geq 56

Divide both sides by

65

\frac{65 sin ( 5 x )}{65} \geq \frac{56}{65}

Simplify

sin (5 x) \geq \frac{56}{65}

sin (5 x) \geq \frac{56}{65}

For

sin (x) \geq a

, if

- 1 < a < 1

then

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

arcsin (\frac{56}{65}) + 2 πn \leq 5 x \leq π - arcsin (\frac{56}{65}) + 2 πn

a \leq u \leq b

then

a \leq u and u \leq b

arcsin (\frac{56}{65}) + 2 πn \leq 5 x and 5 x \leq π - arcsin (\frac{56}{65}) + 2 πn

arcsin (\frac{56}{65}) + 2 πn \leq 5 x : x \geq \frac{arcsin ( \frac{56}{65} )}{5} + \frac{2 πn}{5}

arcsin (\frac{56}{65}) + 2 πn \leq 5 x

Switch sides

5 x \geq arcsin (\frac{56}{65}) + 2 πn

Divide both sides by

5

5 x \geq arcsin (\frac{56}{65}) + 2 πn

Divide both sides by

5

\frac{5 x}{5} \geq \frac{arcsin ( \frac{56}{65} )}{5} + \frac{2 πn}{5}

Simplify

x \geq \frac{arcsin ( \frac{56}{65} )}{5} + \frac{2 πn}{5}

x \geq \frac{arcsin ( \frac{56}{65} )}{5} + \frac{2 πn}{5}

5 x \leq π - arcsin (\frac{56}{65}) + 2 πn : x \leq \frac{π - arcsin ( \frac{56}{65} )}{5} + \frac{2 π}{5} n

5 x \leq π - arcsin (\frac{56}{65}) + 2 πn

Divide both sides by

5

5 x \leq π - arcsin (\frac{56}{65}) + 2 πn

Divide both sides by

5

\frac{5 x}{5} \leq \frac{π}{5} - \frac{arcsin ( \frac{56}{65} )}{5} + \frac{2 πn}{5}

Simplify

x \leq \frac{π}{5} - \frac{arcsin ( \frac{56}{65} )}{5} + \frac{2 πn}{5}

Simplify

\frac{π}{5} - \frac{arcsin ( \frac{56}{65} )}{5} : \frac{π - arcsin ( \frac{56}{65} )}{5}

\frac{π}{5} - \frac{arcsin ( \frac{56}{65} )}{5}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{π - arcsin ( \frac{56}{65} )}{5}

x \leq \frac{π - arcsin ( \frac{56}{65} )}{5} + \frac{2 π}{5} n

x \leq \frac{π - arcsin ( \frac{56}{65} )}{5} + \frac{2 π}{5} n

Combine the intervals

x \geq \frac{arcsin ( \frac{56}{65} )}{5} + \frac{2 πn}{5} and x \leq \frac{π - arcsin ( \frac{56}{65} )}{5} + \frac{2 π}{5} n

Merge Overlapping Intervals

\frac{arcsin ( \frac{56}{65} )}{5} + \frac{2 π}{5} n \leq x \leq \frac{π - arcsin ( \frac{56}{65} )}{5} + \frac{2 π}{5} n

Popular Examples

2sin(x/2)-1<0

2 sin (\frac{x}{2}) - 1 < 0

2sin(2x)+1/2 >= 0

2 sin (2 x) + \frac{1}{2} \geq 0

2sin^2(x)-1<= 0

2 sin^{2} (x) - 1 \leq 0

sin(2x)>= sqrt(3)cos(x)

sin (2 x) \geq 3 cos (x)

(2cos(x)-sqrt(3))<0

(2 cos (x) - 3) < 0