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受欢迎的三角函数 >

cos(x/2)>= 0

解答

cos (\frac{x}{2}) \geq 0

解答

- π + 4 πn \leq x \leq π + 4 πn

+2

间隔符号

[- π + 4 πn, π + 4 πn]

十进制

- 3.14159 \dots + 4 πn \leq x \leq 3.14159 \dots + 4 πn

求解步骤

cos (\frac{x}{2}) \geq 0

对于

cos (x) \geq a

，若

- 1 < a < 1

，则

- arccos (a) + 2 πn \leq x \leq arccos (a) + 2 πn

- arccos (0) + 2 πn \leq \frac{x}{2} \leq arccos (0) + 2 πn

若

a \leq u \leq b

，则

a \leq u and u \leq b

- arccos (0) + 2 πn \leq \frac{x}{2} and \frac{x}{2} \leq arccos (0) + 2 πn

- arccos (0) + 2 πn \leq \frac{x}{2} : x \geq - π + 4 πn

- arccos (0) + 2 πn \leq \frac{x}{2}

交换两边

\frac{x}{2} \geq - arccos (0) + 2 πn

化简

- arccos (0) + 2 πn : - \frac{π}{2} + 2 πn

- arccos (0) + 2 πn

使用以下普通恒等式:

arccos (0) = \frac{π}{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}{2} + 2 πn

\frac{x}{2} \geq - \frac{π}{2} + 2 πn

在两边乘以

2

\frac{x}{2} \geq - \frac{π}{2} + 2 πn

在两边乘以

2

\frac{2 x}{2} \geq - 2 \cdot \frac{π}{2} + 2 \cdot 2 πn

化简

\frac{2 x}{2} \geq - 2 \cdot \frac{π}{2} + 2 \cdot 2 πn

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

- 2 \cdot \frac{π}{2} + 2 \cdot 2 πn : - π + 4 πn

- 2 \cdot \frac{π}{2} + 2 \cdot 2 πn

2 \cdot \frac{π}{2} = π

2 \cdot \frac{π}{2}

分式相乘:

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

= \frac{π 2}{2}

约分:

2

= π

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

数字相乘:

2 \cdot 2 = 4

= 4 πn

= - π + 4 πn

x \geq - π + 4 πn

x \geq - π + 4 πn

x \geq - π + 4 πn

\frac{x}{2} \leq arccos (0) + 2 πn : x \leq π + 4 πn

\frac{x}{2} \leq arccos (0) + 2 πn

化简

arccos (0) + 2 πn : \frac{π}{2} + 2 πn

arccos (0) + 2 πn

使用以下普通恒等式:

arccos (0) = \frac{π}{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}{2} + 2 πn

\frac{x}{2} \leq \frac{π}{2} + 2 πn

在两边乘以

2

\frac{x}{2} \leq \frac{π}{2} + 2 πn

在两边乘以

2

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

化简

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

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

2 \cdot \frac{π}{2} + 2 \cdot 2 πn : π + 4 πn

2 \cdot \frac{π}{2} + 2 \cdot 2 πn

2 \cdot \frac{π}{2} = π

2 \cdot \frac{π}{2}

分式相乘:

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

= \frac{π 2}{2}

约分:

2

= π

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

数字相乘:

2 \cdot 2 = 4

= 4 πn

= π + 4 πn

x \leq π + 4 πn

x \leq π + 4 πn

x \leq π + 4 πn

合并区间

x \geq - π + 4 πn and x \leq π + 4 πn

合并重叠的区间

- π + 4 πn \leq x \leq π + 4 πn

流行的例子

1/2 (10sin(2pi*60x))>-0.52

\frac{1}{2} (10 sin (2 π \cdot 60 x)) > - 0.52

(4cos^2(x)-3)(1-tan^2(x))<= 0

(4 cos^{2} (x) - 3) (1 - tan^{2} (x)) \leq 0

cot(θ)<0,sec(θ)>0

cot (θ) < 0, sec (θ) > 0

cos(θ)>0,cot(θ)>0

cos (θ) > 0, cot (θ) > 0

sec (x) < - 1