zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

cos(x)<0.5

解答

cos (x) < 0.5

解答

\frac{π}{3} + 2 πn < x < \frac{5 π}{3} + 2 πn

+2

间隔符号

(\frac{π}{3} + 2 πn, \frac{5 π}{3} + 2 πn)

十进制

1.04719 \dots + 2 πn < x < 5.23598 \dots + 2 πn

求解步骤

cos (x) < 0.5

对于

cos (x) < a

，若

- 1 < a \leq 1

，则

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

arccos (0.5) + 2 πn < x < 2 π - arccos (0.5) + 2 πn

化简

arccos (0.5) : \frac{π}{3}

arccos (0.5)

= arccos (\frac{1}{2})

使用以下普通恒等式:

arccos (\frac{1}{2}) = \frac{π}{3}

arccos (\frac{1}{2})

x - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arccos (x) π \frac{5 π}{6} \frac{3 π}{4} \frac{2 π}{3} \frac{π}{2} \frac{π}{3} \frac{π}{4} \frac{π}{6} 0 arccos (x) 18 0^{\circ} 15 0^{\circ} 13 5^{\circ} 12 0^{\circ} 9 0^{\circ} 6 0^{\circ} 4 5^{\circ} 3 0^{\circ} 0^{\circ}

= \frac{π}{3}

= \frac{π}{3}

化简

2 π - arccos (0.5) : \frac{5 π}{3}

2 π - arccos (0.5)

arccos (0.5) = \frac{π}{3}

arccos (0.5)

= arccos (\frac{1}{2})

使用以下普通恒等式:

arccos (\frac{1}{2}) = \frac{π}{3}

arccos (\frac{1}{2})

x - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arccos (x) π \frac{5 π}{6} \frac{3 π}{4} \frac{2 π}{3} \frac{π}{2} \frac{π}{3} \frac{π}{4} \frac{π}{6} 0 arccos (x) 18 0^{\circ} 15 0^{\circ} 13 5^{\circ} 12 0^{\circ} 9 0^{\circ} 6 0^{\circ} 4 5^{\circ} 3 0^{\circ} 0^{\circ}

= \frac{π}{3}

= \frac{π}{3}

= 2 π - \frac{π}{3}

化简

2 π - \frac{π}{3}

将项转换为分式:

2 π = \frac{2 π 3}{3}

= \frac{2 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{2 π 3 - π}{3}

2 π 3 - π = 5 π

2 π 3 - π

数字相乘:

2 \cdot 3 = 6

= 6 π - π

同类项相加:

6 π - π = 5 π

= 5 π

= \frac{5 π}{3}

= \frac{5 π}{3}

\frac{π}{3} + 2 πn < x < \frac{5 π}{3} + 2 πn

流行的例子

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

tan (x) \leq 1

4cos(2x)>= 2,0<= x<2pi

4 cos (2 x) \geq 2, 0 \leq x < 2 π

sin (2 x) > cos (x)

cos (x) \leq 1