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受欢迎的三角函数 >

200.4=200+sin(x/(240))

解答

200.4 = 200 + sin (\frac{x}{240})

解答

x = 240 \cdot 0.41151 \dots + 480 πn, x = 240 π - 240 \cdot 0.41151 \dots + 480 πn

+1

度数

x = 5658.76283 \dots^{\circ} + 86399.99999 \dots^{\circ} n, x = 37541.23716 \dots^{\circ} + 86399.99999 \dots^{\circ} n

求解步骤

200.4 = 200 + sin (\frac{x}{240})

交换两边

200 + sin (\frac{x}{240}) = 200.4

将

200

到右边

200 + sin (\frac{x}{240}) = 200.4

两边减去

200

200 + sin (\frac{x}{240}) - 200 = 200.4 - 200

化简

sin (\frac{x}{240}) = 0.4

sin (\frac{x}{240}) = 0.4

使用反三角函数性质

sin (\frac{x}{240}) = 0.4

sin (\frac{x}{240}) = 0.4

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

\frac{x}{240} = arcsin (0.4) + 2 πn, \frac{x}{240} = π - arcsin (0.4) + 2 πn

\frac{x}{240} = arcsin (0.4) + 2 πn, \frac{x}{240} = π - arcsin (0.4) + 2 πn

解

\frac{x}{240} = arcsin (0.4) + 2 πn : x = 240 arcsin (0.4) + 480 πn

\frac{x}{240} = arcsin (0.4) + 2 πn

在两边乘以

240

\frac{x}{240} = arcsin (0.4) + 2 πn

在两边乘以

240

\frac{240 x}{240} = 240 arcsin (0.4) + 240 \cdot 2 πn

化简

x = 240 arcsin (0.4) + 480 πn

x = 240 arcsin (0.4) + 480 πn

解

\frac{x}{240} = π - arcsin (0.4) + 2 πn : x = 240 π - 240 arcsin (0.4) + 480 πn

\frac{x}{240} = π - arcsin (0.4) + 2 πn

在两边乘以

240

\frac{x}{240} = π - arcsin (0.4) + 2 πn

在两边乘以

240

\frac{240 x}{240} = 240 π - 240 arcsin (0.4) + 240 \cdot 2 πn

化简

x = 240 π - 240 arcsin (0.4) + 480 πn

x = 240 π - 240 arcsin (0.4) + 480 πn

x = 240 arcsin (0.4) + 480 πn, x = 240 π - 240 arcsin (0.4) + 480 πn

以小数形式表示解

x = 240 \cdot 0.41151 \dots + 480 πn, x = 240 π - 240 \cdot 0.41151 \dots + 480 πn

作图

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