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受欢迎的三角函数 >

2csc(x)+7/(cos(x))=0

解答

2 csc (x) + \frac{7}{cos ( x )} = 0

解答

x = 2.86329 \dots + πn

+1

度数

x = 164.05460 \dots^{\circ} + 18 0^{\circ} n

求解步骤

2 csc (x) + \frac{7}{cos ( x )} = 0

化简

2 csc (x) + \frac{7}{cos ( x )} : \frac{2 csc ( x ) cos ( x ) + 7}{cos ( x )}

2 csc (x) + \frac{7}{cos ( x )}

将项转换为分式:

2 csc (x) = \frac{2 csc ( x ) cos ( x )}{cos ( x )}

= \frac{2 csc ( x ) cos ( x )}{cos ( x )} + \frac{7}{cos ( x )}

因为分母相等，所以合并分式:

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

= \frac{2 csc ( x ) cos ( x ) + 7}{cos ( x )}

\frac{2 csc ( x ) cos ( x ) + 7}{cos ( x )} = 0

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

2 csc (x) cos (x) + 7 = 0

使用三角恒等式改写

2 csc (x) cos (x) + 7

csc (x) cos (x) = cot (x)

csc (x) cos (x)

用 sin, cos 表示

csc (x) cos (x)

使用基本三角恒等式:

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

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

化简

\frac{1}{sin ( x )} cos (x) : \frac{cos ( x )}{sin ( x )}

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

分式相乘:

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

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

乘以:

1 \cdot cos (x) = cos (x)

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

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

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

使用基本三角恒等式:

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

= cot (x)

= 7 + 2 cot (x)

7 + 2 cot (x) = 0

将

7

到右边

7 + 2 cot (x) = 0

两边减去

7

7 + 2 cot (x) - 7 = 0 - 7

化简

2 cot (x) = - 7

2 cot (x) = - 7

两边除以

2

2 cot (x) = - 7

两边除以

2

\frac{2 cot ( x )}{2} = \frac{- 7}{2}

化简

cot (x) = - \frac{7}{2}

cot (x) = - \frac{7}{2}

使用反三角函数性质

cot (x) = - \frac{7}{2}

cot (x) = - \frac{7}{2}

的通解

cot (x) = - a \Rightarrow x = arccot (- a) + πn

x = arccot (- \frac{7}{2}) + πn

x = arccot (- \frac{7}{2}) + πn

以小数形式表示解

x = 2.86329 \dots + πn

作图

流行的例子

csc (θ) = \frac{13}{6}

(tan(θ)cot(θ))/(sec^2(θ))=cot(θ)

\frac{tan ( θ ) cot ( θ )}{sec ^{2} ( θ )} = cot (θ)

sin(y)=(sqrt(3))/2

sin (y) = \frac{3}{2}

9sin^2(x)+3cos(x)-7=0

9 sin^{2} (x) + 3 cos (x) - 7 = 0

3 sec (2 x + 3) = 4