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Popular >

3sin(x)<= 3/2

Solution

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

- \frac{7 π}{6} + 2 πn \leq x \leq \frac{π}{6} + 2 πn

Interval Notation

[- \frac{7 π}{6} + 2 πn, \frac{π}{6} + 2 πn]

Decimal Notation

- 3.66519 \dots + 2 πn \leq x \leq 0.52359 \dots + 2 πn

Solution steps

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

Divide both sides by

3

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

Divide both sides by

3

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

Simplify

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

Simplify

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

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

Divide the numbers:

\frac{3}{3} = 1

= sin (x)

Simplify

\frac{\frac{3}{2}}{3} : \frac{1}{2}

\frac{\frac{3}{2}}{3}

Apply the fraction rule:

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

= \frac{3}{2 \cdot 3}

Multiply the numbers:

2 \cdot 3 = 6

= \frac{3}{6}

Cancel the common factor:

3

= \frac{1}{2}

sin (x) \leq \frac{1}{2}

sin (x) \leq \frac{1}{2}

sin (x) \leq \frac{1}{2}

For

sin (x) \leq a

, if

- 1 < a < 1

then

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

- π - arcsin (\frac{1}{2}) + 2 πn \leq x \leq arcsin (\frac{1}{2}) + 2 πn

Simplify

- π - arcsin (\frac{1}{2}) : - \frac{7 π}{6}

- π - arcsin (\frac{1}{2})

Use the following trivial identity:

arcsin (\frac{1}{2}) = \frac{π}{6}

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 - \frac{π}{6}

Simplify

- π - \frac{π}{6}

Convert element to fraction:

π = \frac{π 6}{6}

= - \frac{π 6}{6} - \frac{π}{6}

Since the denominators are equal, combine the fractions:

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

= \frac{- π 6 - π}{6}

Add similar elements:

- 6 π - π = - 7 π

= \frac{- 7 π}{6}

Apply the fraction rule:

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

= - \frac{7 π}{6}

= - \frac{7 π}{6}

Simplify

arcsin (\frac{1}{2}) : \frac{π}{6}

arcsin (\frac{1}{2})

Use the following trivial identity:

arcsin (\frac{1}{2}) = \frac{π}{6}

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}

= \frac{π}{6}

- \frac{7 π}{6} + 2 πn \leq x \leq \frac{π}{6} + 2 πn

tan (x) > - 1

\frac{π}{2} - arctan (n) \leq 0.001

x, \frac{10}{cos ( x )} > 10

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

sin^{2} (x) \geq 0