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受欢迎的三角函数 >

cos(2x)=-0.4,-180<= x<= 180

解答

cos (2 x) = - 0.4, - 18 0^{\circ} \leq x \leq 18 0^{\circ}

解答

x = 0.99115 \dots, x = - 0.99115 \dots, x = 2.15043 \dots, x = - 2.15043 \dots

求解步骤

cos (2 x) = - 0.4, - 18 0^{\circ} \leq x \leq 18 0^{\circ}

使用反三角函数性质

cos (2 x) = - 0.4

cos (2 x) = - 0.4

的通解

cos (x) = - a \Rightarrow x = arccos (- a) + 36 0^{\circ} n, x = - arccos (- a) + 36 0^{\circ} n

2 x = arccos (- 0.4) + 36 0^{\circ} n, 2 x = - arccos (- 0.4) + 36 0^{\circ} n

2 x = arccos (- 0.4) + 36 0^{\circ} n, 2 x = - arccos (- 0.4) + 36 0^{\circ} n

解

2 x = arccos (- 0.4) + 36 0^{\circ} n : x = \frac{arccos ( - 0.4 )}{2} + 18 0^{\circ} n

2 x = arccos (- 0.4) + 36 0^{\circ} n

两边除以

2

2 x = arccos (- 0.4) + 36 0^{\circ} n

两边除以

2

\frac{2 x}{2} = \frac{arccos ( - 0.4 )}{2} + \frac{36 0 ^{\circ} n}{2}

化简

x = \frac{arccos ( - 0.4 )}{2} + 18 0^{\circ} n

x = \frac{arccos ( - 0.4 )}{2} + 18 0^{\circ} n

解

2 x = - arccos (- 0.4) + 36 0^{\circ} n : x = - \frac{arccos ( - 0.4 )}{2} + 18 0^{\circ} n

2 x = - arccos (- 0.4) + 36 0^{\circ} n

两边除以

2

2 x = - arccos (- 0.4) + 36 0^{\circ} n

两边除以

2

\frac{2 x}{2} = - \frac{arccos ( - 0.4 )}{2} + \frac{36 0 ^{\circ} n}{2}

化简

x = - \frac{arccos ( - 0.4 )}{2} + 18 0^{\circ} n

x = - \frac{arccos ( - 0.4 )}{2} + 18 0^{\circ} n

x = \frac{arccos ( - 0.4 )}{2} + 18 0^{\circ} n, x = - \frac{arccos ( - 0.4 )}{2} + 18 0^{\circ} n

在

- 18 0^{\circ} \leq x \leq 18 0^{\circ}

范围内的解

x = 0.99115 \dots, x = - 0.99115 \dots, x = 2.15043 \dots, x = - 2.15043 \dots

作图

流行的例子

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cos (x) = \frac{- 4}{\frac{8}{3} 3}

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