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受欢迎的三角函数 >

5^{5-3csc(θ)}=1

解答

5^{5 - 3 c s c (θ)} = 1

解答

θ = 0.64350 \dots + 2 πn, θ = π - 0.64350 \dots + 2 πn

+1

度数

θ = 36.86989 \dots^{\circ} + 36 0^{\circ} n, θ = 143.13010 \dots^{\circ} + 36 0^{\circ} n

求解步骤

5^{5 - 3 c s c (θ)} = 1

使用指数运算法则

5^{5 - 3 c s c (θ)} = 1

若

f (x) = g (x)

，则

ln (f (x)) = ln (g (x))

ln (5^{5 - 3 c s c (θ)}) = ln (1)

使用对数计算法则:

ln (x^{a}) = a \cdot ln (x)

ln (5^{5 - 3 c s c (θ)}) = (5 - 3 csc (θ)) ln (5)

(5 - 3 csc (θ)) ln (5) = ln (1)

(5 - 3 csc (θ)) ln (5) = ln (1)

解

(5 - 3 csc (θ)) ln (5) = ln (1) : csc (θ) = \frac{5}{3}

(5 - 3 csc (θ)) ln (5) = ln (1)

两边除以

ln (5)

(5 - 3 csc (θ)) ln (5) = ln (1)

两边除以

ln (5)

\frac{( 5 - 3 csc ( θ ) ) ln ( 5 )}{ln ( 5 )} = \frac{ln ( 1 )}{ln ( 5 )}

化简

\frac{( 5 - 3 csc ( θ ) ) ln ( 5 )}{ln ( 5 )} = \frac{ln ( 1 )}{ln ( 5 )}

化简

\frac{( 5 - 3 csc ( θ ) ) ln ( 5 )}{ln ( 5 )} : 5 - 3 csc (θ)

\frac{( 5 - 3 csc ( θ ) ) ln ( 5 )}{ln ( 5 )}

约分:

ln (5)

= 5 - 3 csc (θ)

化简

\frac{ln ( 1 )}{ln ( 5 )} : 0

\frac{ln ( 1 )}{ln ( 5 )}

化简

ln (1) : 0

ln (1)

使用对数计算法则:

lo g_{a} (1) = 0

= 0

= \frac{0}{ln ( 5 )}

使用法则

\frac{0}{a} = 0, a \neq = 0

= 0

5 - 3 csc (θ) = 0

5 - 3 csc (θ) = 0

5 - 3 csc (θ) = 0

将

5

到右边

5 - 3 csc (θ) = 0

两边减去

5

5 - 3 csc (θ) - 5 = 0 - 5

化简

- 3 csc (θ) = - 5

- 3 csc (θ) = - 5

两边除以

- 3

- 3 csc (θ) = - 5

两边除以

- 3

\frac{- 3 csc ( θ )}{- 3} = \frac{- 5}{- 3}

化简

csc (θ) = \frac{5}{3}

csc (θ) = \frac{5}{3}

csc (θ) = \frac{5}{3}

使用反三角函数性质

csc (θ) = \frac{5}{3}

csc (θ) = \frac{5}{3}

的通解

csc (x) = a \Rightarrow x = arccsc (a) + 2 πn, x = π - arccsc (a) + 2 πn

θ = arccsc (\frac{5}{3}) + 2 πn, θ = π - arccsc (\frac{5}{3}) + 2 πn

θ = arccsc (\frac{5}{3}) + 2 πn, θ = π - arccsc (\frac{5}{3}) + 2 πn

以小数形式表示解

θ = 0.64350 \dots + 2 πn, θ = π - 0.64350 \dots + 2 πn

作图

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