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受欢迎的三角函数 >

4cot(x)=sqrt(3)csc(x)

解答

4 cot (x) = 3 csc (x)

解答

x = 1.12296 \dots + 2 πn, x = 2 π - 1.12296 \dots + 2 πn

+1

度数

x = 64.34109 \dots^{\circ} + 36 0^{\circ} n, x = 295.65890 \dots^{\circ} + 36 0^{\circ} n

求解步骤

4 cot (x) = 3 csc (x)

两边减去

3 csc (x)

4 cot (x) - 3 csc (x) = 0

用 sin, cos 表示

4 cot (x) - csc (x) 3

使用基本三角恒等式:

cot (x) = \frac{cos ( x )}{sin ( x )}

= 4 \cdot \frac{cos ( x )}{sin ( x )} - csc (x) 3

使用基本三角恒等式:

csc (x) = \frac{1}{sin ( x )}

= 4 \cdot \frac{cos ( x )}{sin ( x )} - \frac{1}{sin ( x )} 3

化简

4 \cdot \frac{cos ( x )}{sin ( x )} - \frac{1}{sin ( x )} 3 : \frac{4 cos ( x ) - 3}{sin ( x )}

4 \cdot \frac{cos ( x )}{sin ( x )} - \frac{1}{sin ( x )} 3

4 \cdot \frac{cos ( x )}{sin ( x )} = \frac{4 cos ( x )}{sin ( x )}

4 \cdot \frac{cos ( x )}{sin ( x )}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{cos ( x ) \cdot 4}{sin ( x )}

\frac{1}{sin ( x )} 3 = \frac{3}{sin ( x )}

\frac{1}{sin ( x )} 3

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 3}{sin ( x )}

乘以:

1 \cdot 3 = 3

= \frac{3}{sin ( x )}

= \frac{4 cos ( x )}{sin ( x )} - \frac{3}{sin ( x )}

使用法则

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{4 cos ( x ) - 3}{sin ( x )}

= \frac{4 cos ( x ) - 3}{sin ( x )}

\frac{- 3 + 4 cos ( x )}{sin ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

- 3 + 4 cos (x) = 0

将

3

到右边

- 3 + 4 cos (x) = 0

两边加上

3

- 3 + 4 cos (x) + 3 = 0 + 3

化简

4 cos (x) = 3

4 cos (x) = 3

两边除以

4

4 cos (x) = 3

两边除以

4

\frac{4 cos ( x )}{4} = \frac{3}{4}

化简

cos (x) = \frac{3}{4}

cos (x) = \frac{3}{4}

使用反三角函数性质

cos (x) = \frac{3}{4}

cos (x) = \frac{3}{4}

的通解

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

x = arccos (\frac{3}{4}) + 2 πn, x = 2 π - arccos (\frac{3}{4}) + 2 πn

x = arccos (\frac{3}{4}) + 2 πn, x = 2 π - arccos (\frac{3}{4}) + 2 πn

以小数形式表示解

x = 1.12296 \dots + 2 πn, x = 2 π - 1.12296 \dots + 2 πn

作图

流行的例子

sin (θ) = \frac{7}{15}

cos(x)=(sqrt(5))/3

cos (x) = \frac{5}{3}

cos (x) = - \frac{7}{8}

sin(x)=-cos(2x)

sin (x) = - cos (2 x)

csc(pi/(24)x)=1

csc (\frac{π}{24} x) = 1