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受欢迎的三角函数 >

2.55= 1/(tan(x))

解答

2.55 = \frac{1}{tan ( x )}

解答

x = 0.37372 \dots + πn

+1

度数

x = 21.41296 \dots^{\circ} + 18 0^{\circ} n

求解步骤

2.55 = \frac{1}{tan ( x )}

交换两边

\frac{1}{tan ( x )} = 2.55

在两边乘以

tan (x)

\frac{1}{tan ( x )} = 2.55

在两边乘以

tan (x)

\frac{1}{tan ( x )} tan (x) = 2.55 tan (x)

化简

1 = 2.55 tan (x)

1 = 2.55 tan (x)

交换两边

2.55 tan (x) = 1

在两边乘以

100

2.55 tan (x) = 1

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

2.55 tan (x) \cdot 100 = 1 \cdot 100

整理后得

255 tan (x) = 100

255 tan (x) = 100

两边除以

255

255 tan (x) = 100

两边除以

255

\frac{255 tan ( x )}{255} = \frac{100}{255}

化简

tan (x) = \frac{20}{51}

tan (x) = \frac{20}{51}

验证解

找到无定义的点（奇点）:

tan (x) = 0

取

\frac{1}{tan ( x )}

的分母，令其等于零

tan (x) = 0

以下点无定义

tan (x) = 0

将不在定义域的点与解相综合:

tan (x) = \frac{20}{51}

使用反三角函数性质

tan (x) = \frac{20}{51}

tan (x) = \frac{20}{51}

的通解

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan (\frac{20}{51}) + πn

x = arctan (\frac{20}{51}) + πn

以小数形式表示解

x = 0.37372 \dots + πn

作图

流行的例子

tan (5 x) = cot (x)

1/4 sin(8x)=-1/8 ,2cos(8x)=sqrt(3)

\frac{1}{4} sin (8 x) = - \frac{1}{8}, 2 cos (8 x) = 3

sin(x)-sin(2x)=0,0<= x<2pi

sin (x) - sin (2 x) = 0, 0 \leq x < 2 π

sin(2x)=(-2sqrt(6))/7

sin (2 x) = \frac{- 2 6}{7}

arctan(4x)+arctan(6x)=90

arctan (4 x) + arctan (6 x) = 90