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受欢迎的三角函数 >

sin(5x-1)= 4/5

解答

sin (5 x - 1) = \frac{4}{5}

解答

x = \frac{0.92729 \dots}{5} + \frac{2 πn}{5} + \frac{1}{5}, x = \frac{π}{5} - \frac{0.92729 \dots}{5} + \frac{2 πn}{5} + \frac{1}{5}

+1

度数

x = 22.08517 \dots^{\circ} + 7 2^{\circ} n, x = 36.83313 \dots^{\circ} + 7 2^{\circ} n

求解步骤

sin (5 x - 1) = \frac{4}{5}

使用反三角函数性质

sin (5 x - 1) = \frac{4}{5}

sin (5 x - 1) = \frac{4}{5}

的通解

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

5 x - 1 = arcsin (\frac{4}{5}) + 2 πn, 5 x - 1 = π - arcsin (\frac{4}{5}) + 2 πn

5 x - 1 = arcsin (\frac{4}{5}) + 2 πn, 5 x - 1 = π - arcsin (\frac{4}{5}) + 2 πn

解

5 x - 1 = arcsin (\frac{4}{5}) + 2 πn : x = \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

5 x - 1 = arcsin (\frac{4}{5}) + 2 πn

将

1

到右边

5 x - 1 = arcsin (\frac{4}{5}) + 2 πn

两边加上

1

5 x - 1 + 1 = arcsin (\frac{4}{5}) + 2 πn + 1

化简

5 x = arcsin (\frac{4}{5}) + 2 πn + 1

5 x = arcsin (\frac{4}{5}) + 2 πn + 1

两边除以

5

5 x = arcsin (\frac{4}{5}) + 2 πn + 1

两边除以

5

\frac{5 x}{5} = \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

化简

x = \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

x = \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

解

5 x - 1 = π - arcsin (\frac{4}{5}) + 2 πn : x = \frac{π}{5} - \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

5 x - 1 = π - arcsin (\frac{4}{5}) + 2 πn

将

1

到右边

5 x - 1 = π - arcsin (\frac{4}{5}) + 2 πn

两边加上

1

5 x - 1 + 1 = π - arcsin (\frac{4}{5}) + 2 πn + 1

化简

5 x = π - arcsin (\frac{4}{5}) + 2 πn + 1

5 x = π - arcsin (\frac{4}{5}) + 2 πn + 1

两边除以

5

5 x = π - arcsin (\frac{4}{5}) + 2 πn + 1

两边除以

5

\frac{5 x}{5} = \frac{π}{5} - \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

化简

x = \frac{π}{5} - \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

x = \frac{π}{5} - \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

x = \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}, x = \frac{π}{5} - \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

以小数形式表示解

x = \frac{0.92729 \dots}{5} + \frac{2 πn}{5} + \frac{1}{5}, x = \frac{π}{5} - \frac{0.92729 \dots}{5} + \frac{2 πn}{5} + \frac{1}{5}

作图

流行的例子

sin^{2} (x) = \frac{1}{36}

tan (x) = 31

sin^4(x)+cos^2(x)=2

sin^{4} (x) + cos^{2} (x) = 2

5tan(x)=15cot(x)

5 tan (x) = 15 cot (x)

solvefor x,arctan(x)=arctan(y)

so l v e f or x, arctan (x) = arctan (y)