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受欢迎的三角函数 >

7sin(5x)=2

解答

7 sin (5 x) = 2

解答

x = \frac{0.28975 \dots}{5} + \frac{2 πn}{5}, x = \frac{π}{5} - \frac{0.28975 \dots}{5} + \frac{2 πn}{5}

+1

度数

x = 3.32030 \dots^{\circ} + 7 2^{\circ} n, x = 32.67969 \dots^{\circ} + 7 2^{\circ} n

求解步骤

7 sin (5 x) = 2

两边除以

7

7 sin (5 x) = 2

两边除以

7

\frac{7 sin ( 5 x )}{7} = \frac{2}{7}

化简

sin (5 x) = \frac{2}{7}

sin (5 x) = \frac{2}{7}

使用反三角函数性质

sin (5 x) = \frac{2}{7}

sin (5 x) = \frac{2}{7}

的通解

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

5 x = arcsin (\frac{2}{7}) + 2 πn, 5 x = π - arcsin (\frac{2}{7}) + 2 πn

5 x = arcsin (\frac{2}{7}) + 2 πn, 5 x = π - arcsin (\frac{2}{7}) + 2 πn

解

5 x = arcsin (\frac{2}{7}) + 2 πn : x = \frac{arcsin ( \frac{2}{7} )}{5} + \frac{2 πn}{5}

5 x = arcsin (\frac{2}{7}) + 2 πn

两边除以

5

5 x = arcsin (\frac{2}{7}) + 2 πn

两边除以

5

\frac{5 x}{5} = \frac{arcsin ( \frac{2}{7} )}{5} + \frac{2 πn}{5}

化简

x = \frac{arcsin ( \frac{2}{7} )}{5} + \frac{2 πn}{5}

x = \frac{arcsin ( \frac{2}{7} )}{5} + \frac{2 πn}{5}

解

5 x = π - arcsin (\frac{2}{7}) + 2 πn : x = \frac{π}{5} - \frac{arcsin ( \frac{2}{7} )}{5} + \frac{2 πn}{5}

5 x = π - arcsin (\frac{2}{7}) + 2 πn

两边除以

5

5 x = π - arcsin (\frac{2}{7}) + 2 πn

两边除以

5

\frac{5 x}{5} = \frac{π}{5} - \frac{arcsin ( \frac{2}{7} )}{5} + \frac{2 πn}{5}

化简

x = \frac{π}{5} - \frac{arcsin ( \frac{2}{7} )}{5} + \frac{2 πn}{5}

x = \frac{π}{5} - \frac{arcsin ( \frac{2}{7} )}{5} + \frac{2 πn}{5}

x = \frac{arcsin ( \frac{2}{7} )}{5} + \frac{2 πn}{5}, x = \frac{π}{5} - \frac{arcsin ( \frac{2}{7} )}{5} + \frac{2 πn}{5}

以小数形式表示解

x = \frac{0.28975 \dots}{5} + \frac{2 πn}{5}, x = \frac{π}{5} - \frac{0.28975 \dots}{5} + \frac{2 πn}{5}

作图

流行的例子

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cos(pi/2-x)= 4/5

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