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受欢迎的三角函数 >

sin(x)<= (sqrt(2))/2

解答

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

解答

- \frac{5 π}{4} + 2 πn \leq x \leq \frac{π}{4} + 2 πn

+2

间隔符号

[- \frac{5 π}{4} + 2 πn, \frac{π}{4} + 2 πn]

十进制

- 3.92699 \dots + 2 πn \leq x \leq 0.78539 \dots + 2 πn

求解步骤

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

对于

sin (x) \leq a

，若

- 1 < a < 1

，则

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

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

化简

- π - arcsin (\frac{2}{2}) : - \frac{5 π}{4}

- π - arcsin (\frac{2}{2})

使用以下普通恒等式:

arcsin (\frac{2}{2}) = \frac{π}{4}

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}{4}

化简

- π - \frac{π}{4}

将项转换为分式:

π = \frac{π 4}{4}

= - \frac{π 4}{4} - \frac{π}{4}

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 4 - π}{4}

同类项相加:

- 4 π - π = - 5 π

= \frac{- 5 π}{4}

使用分式法则:

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

= - \frac{5 π}{4}

= - \frac{5 π}{4}

化简

arcsin (\frac{2}{2}) : \frac{π}{4}

arcsin (\frac{2}{2})

使用以下普通恒等式:

arcsin (\frac{2}{2}) = \frac{π}{4}

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}{4}

- \frac{5 π}{4} + 2 πn \leq x \leq \frac{π}{4} + 2 πn

流行的例子

tan(x)-cot(x)>0

tan (x) - cot (x) > 0

sin^2(x)+cos(x)>= 1

sin^{2} (x) + cos (x) \geq 1

cos(x)>= (sqrt(3))/2

cos (x) \geq \frac{3}{2}

cos (x) - 1 \geq 0

2 sin (\frac{x}{2}) - 1 > 0