en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(4x+17)>0

Solution

sin (4 x + 1 7^{\circ}) > 0

Solution

- \frac{1 7 ^{\circ}}{4} + \frac{π}{2} n < x < \frac{π - 1 7 ^{\circ}}{4} + \frac{π}{2} n

+2

Interval Notation

(- \frac{1 7 ^{\circ}}{4} + \frac{π}{2} n, \frac{π - 1 7 ^{\circ}}{4} + \frac{π}{2} n)

Decimal Notation

- 0.07417 \dots + \frac{π}{2} n < x < 0.71122 \dots + \frac{π}{2} n

Solution steps

sin (4 x + 1 7^{\circ}) > 0

For

sin (x) > a

, if

- 1 \leq a < 1

then

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

arcsin (0) + 2 πn < (4 x + 1 7^{\circ}) < π - arcsin (0) + 2 πn

If

a < u < b

then

a < u and u < b

arcsin (0) + 2 πn < 4 x + 1 7^{\circ} and 4 x + 1 7^{\circ} < π - arcsin (0) + 2 πn

arcsin (0) + 2 πn < 4 x + 1 7^{\circ} : x > \frac{πn}{2} - \frac{1 7 ^{\circ}}{4}

arcsin (0) + 2 πn < 4 x + 1 7^{\circ}

Switch sides

4 x + 1 7^{\circ} > arcsin (0) + 2 πn

Simplify

arcsin (0) + 2 πn : 2 πn

arcsin (0) + 2 πn

Use the following trivial identity:

arcsin (0) = 0

x 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arcsin (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} arcsin (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ}

= 0 + 2 πn

0 + 2 πn = 2 πn

= 2 πn

4 x + 1 7^{\circ} > 2 πn

Move

1 7^{\circ}

to the right side

4 x + 1 7^{\circ} > 2 πn

Subtract

1 7^{\circ}

from both sides

4 x + 1 7^{\circ} - 1 7^{\circ} > 2 πn - 1 7^{\circ}

Simplify

4 x > 2 πn - 1 7^{\circ}

4 x > 2 πn - 1 7^{\circ}

Divide both sides by

4

4 x > 2 πn - 1 7^{\circ}

Divide both sides by

4

\frac{4 x}{4} > \frac{2 πn}{4} - \frac{1 7 ^{\circ}}{4}

Simplify

x > \frac{πn}{2} - \frac{1 7 ^{\circ}}{4}

x > \frac{πn}{2} - \frac{1 7 ^{\circ}}{4}

4 x + 1 7^{\circ} < π - arcsin (0) + 2 πn : x < \frac{π - 1 7 ^{\circ}}{4} + \frac{π}{2} n

4 x + 1 7^{\circ} < π - arcsin (0) + 2 πn

Simplify

π - arcsin (0) + 2 πn : π + 2 πn

π - arcsin (0) + 2 πn

Use the following trivial identity:

arcsin (0) = 0

x 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arcsin (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} arcsin (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ}

= π - 0 + 2 πn

π - 0 + 2 πn = π + 2 πn

= π + 2 πn

4 x + 1 7^{\circ} < π + 2 πn

Move

1 7^{\circ}

to the right side

4 x + 1 7^{\circ} < π + 2 πn

Subtract

1 7^{\circ}

from both sides

4 x + 1 7^{\circ} - 1 7^{\circ} < π + 2 πn - 1 7^{\circ}

Simplify

4 x < π + 2 πn - 1 7^{\circ}

4 x < π + 2 πn - 1 7^{\circ}

Divide both sides by

4

4 x < π + 2 πn - 1 7^{\circ}

Divide both sides by

4

\frac{4 x}{4} < \frac{π}{4} + \frac{2 πn}{4} - \frac{1 7 ^{\circ}}{4}

Simplify

x < \frac{π}{4} + \frac{πn}{2} - \frac{1 7 ^{\circ}}{4}

Simplify

\frac{π}{4} - \frac{1 7 ^{\circ}}{4} : \frac{π - 1 7 ^{\circ}}{4}

\frac{π}{4} - \frac{1 7 ^{\circ}}{4}

Apply rule

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

= \frac{π - 1 7 ^{\circ}}{4}

x < \frac{π - 1 7 ^{\circ}}{4} + \frac{π}{2} n

x < \frac{π - 1 7 ^{\circ}}{4} + \frac{π}{2} n

Combine the intervals

x > \frac{πn}{2} - \frac{1 7 ^{\circ}}{4} and x < \frac{π - 1 7 ^{\circ}}{4} + \frac{π}{2} n

Merge Overlapping Intervals

- \frac{1 7 ^{\circ}}{4} + \frac{π}{2} n < x < \frac{π - 1 7 ^{\circ}}{4} + \frac{π}{2} n

Popular Examples

3sin((pix)/(12)-pi/2)<=-2

3 sin (\frac{π x}{12} - \frac{π}{2}) \leq - 2

-sin(x)(2+sin(x))-cos^2(x)>0

- sin (x) (2 + sin (x)) - cos^{2} (x) > 0

sin(pi/6)cos(x)+cos(pi/6)sin(x)<= 1

sin (\frac{π}{6}) cos (x) + cos (\frac{π}{6}) sin (x) \leq 1

1/(sqrt(3))<tan(x)

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

6 cos (θ) \geq 0