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受欢迎的三角函数 >

solvefor a,45=arctanh(a/b)

解答

求解

a, 45 = arctanh (\frac{a}{b})

解答

a = \emptyset b

求解步骤

45 = arctanh (\frac{a}{b})

交换两边

arctanh (\frac{a}{b}) = 45

两边减去

45

arctanh (\frac{a}{b}) - 45 = 0

用替代法求解

arctanh (\frac{a}{b}) - 45 = 0

令

: arctanh (\frac{a}{b}) = u

u - 45 = 0

u - 45 = 0 : u = 45

u - 45 = 0

将

45

到右边

u - 45 = 0

两边加上

45

u - 45 + 45 = 0 + 45

化简

u = 45

u = 45

arctanh (\frac{a}{b}) = 45

u = arctanh (\frac{a}{b})

代回

arctanh (\frac{a}{b}) = 45

arctanh (\frac{a}{b}) = 45

令

: u = \frac{a}{b}

arctanh (u) - 45 = 0

用替代法求解

arctanh (u) - 45 = 0

令

: arctanh (u) = u

u - 45 = 0

u - 45 = 0 : u = 45

u - 45 = 0

将

45

到右边

u - 45 = 0

两边加上

45

u - 45 + 45 = 0 + 45

化简

u = 45

u = 45

u = arctanh (u)

代回

arctanh (u) = 45

arctanh (u) = 45

使用三角恒等式改写

- 45 + arctanh (u)

使用双曲函数恒等式:

arctanh (x) = \frac{ln ( \frac{1 + x}{1 - x} )}{2}

= - 45 + \frac{ln ( \frac{1 + u}{1 - u} )}{2}

- 45 + \frac{ln ( \frac{1 + u}{1 - u} )}{2} = 0

将

45

到右边

- 45 + \frac{ln ( \frac{1 + u}{1 - u} )}{2} = 0

两边加上

45

- 45 + \frac{ln ( \frac{1 + u}{1 - u} )}{2} + 45 = 0 + 45

化简

\frac{ln ( \frac{1 + u}{1 - u} )}{2} = 45

\frac{ln ( \frac{1 + u}{1 - u} )}{2} = 45

在两边乘以

2

\frac{ln ( \frac{1 + u}{1 - u} )}{2} = 45

在两边乘以

2

\frac{2 ln ( \frac{1 + u}{1 - u} )}{2} = 45 \cdot 2

化简

ln (\frac{1 + u}{1 - u}) = 90

ln (\frac{1 + u}{1 - u}) = 90

使用反三角函数性质

ln (\frac{1 + u}{1 - u}) = 90

ln (\frac{1 + u}{1 - u}) = 90

的通解

无解

u = \frac{a}{b}

代回

\frac{a}{b} = \emptyset : a = \emptyset b; b \neq = 0

\frac{a}{b} = \emptyset

在两边乘以

b

\frac{a}{b} = \emptyset

在两边乘以

b

\frac{ab}{b} = \emptyset b; b \neq = 0

化简

a = \emptyset b; b \neq = 0

a = \emptyset b; b \neq = 0

a = \emptyset b

作图

流行的例子

solvefor x,sec(x)=3

so l v e f or x, sec (x) = 3

cot(θ-30)= 1/(sqrt(3))

cot (θ - 3 0^{\circ}) = \frac{1}{3}

(cot(x)-sqrt(3))(csc(x)+2)=0

(cot (x) - 3) (csc (x) + 2) = 0

sin(x)= 7/(9.4)

sin (x) = \frac{7}{9.4}

cos (x) = \frac{6}{11}