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受欢迎的三角函数 >

sin(x)>= 0.5sqrt(3)

解答

sin (x) \geq 0.5 3

解答

\frac{π}{3} + 2 πn \leq x \leq \frac{2 π}{3} + 2 πn

+2

间隔符号

[\frac{π}{3} + 2 πn, \frac{2 π}{3} + 2 πn]

十进制

1.04719 \dots + 2 πn \leq x \leq 2.09439 \dots + 2 πn

求解步骤

sin (x) \geq 0.5 3

对于

sin (x) \geq a

，若

- 1 < a < 1

，则

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

arcsin (0.5 3) + 2 πn \leq x \leq π - arcsin (0.5 3) + 2 πn

化简

arcsin (0.5 3) : \frac{π}{3}

arcsin (0.5 3)

= arcsin (3 \frac{1}{2})

使用以下普通恒等式:

arcsin (3 \frac{1}{2}) = \frac{π}{3}

arcsin (3 \frac{1}{2})

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}{3}

= \frac{π}{3}

化简

π - arcsin (0.5 3) : \frac{2 π}{3}

π - arcsin (0.5 3)

arcsin (0.5 3) = \frac{π}{3}

arcsin (0.5 3)

= arcsin (3 \frac{1}{2})

使用以下普通恒等式:

arcsin (3 \frac{1}{2}) = \frac{π}{3}

arcsin (3 \frac{1}{2})

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}{3}

= \frac{π}{3}

= π - \frac{π}{3}

化简

π - \frac{π}{3}

将项转换为分式:

π = \frac{π 3}{3}

= \frac{π 3}{3} - \frac{π}{3}

因为分母相等，所以合并分式:

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

= \frac{π 3 - π}{3}

同类项相加:

3 π - π = 2 π

= \frac{2 π}{3}

= \frac{2 π}{3}

\frac{π}{3} + 2 πn \leq x \leq \frac{2 π}{3} + 2 πn

流行的例子

((sin(x)-cos(x)+3sqrt(2)))/(sqrt(2))>0

\frac{( sin ( x ) - cos ( x ) + 3 2 )}{2} > 0

sin(x)(1-sin(x))>0

sin (x) (1 - sin (x)) > 0

(-1/5)*cos(2 pi/5 (x+1))+1>= 16/15

(- \frac{1}{5}) \cdot cos (2 \frac{π}{5} (x + 1)) + 1 \geq \frac{16}{15}

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

cos^{2} (x) \geq sin^{2} (x)

cos (x) > 2