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受欢迎的三角函数 >

(cot(θ))/(csc(θ))=sin(θ)

解答

\frac{cot ( θ )}{csc ( θ )} = sin (θ)

解答

θ = \frac{π}{4} + πn

+1

度数

θ = 4 5^{\circ} + 18 0^{\circ} n

求解步骤

\frac{cot ( θ )}{csc ( θ )} = sin (θ)

两边减去

sin (θ)

\frac{cot ( θ )}{csc ( θ )} - sin (θ) = 0

化简

\frac{cot ( θ )}{csc ( θ )} - sin (θ) : \frac{cot ( θ ) - sin ( θ ) csc ( θ )}{csc ( θ )}

\frac{cot ( θ )}{csc ( θ )} - sin (θ)

将项转换为分式:

sin (θ) = \frac{sin ( θ ) csc ( θ )}{csc ( θ )}

= \frac{cot ( θ )}{csc ( θ )} - \frac{sin ( θ ) csc ( θ )}{csc ( θ )}

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{cot ( θ ) - sin ( θ ) csc ( θ )}{csc ( θ )}

\frac{cot ( θ ) - sin ( θ ) csc ( θ )}{csc ( θ )} = 0

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

cot (θ) - sin (θ) csc (θ) = 0

使用三角恒等式改写

cot (θ) - sin (θ) csc (θ)

csc (θ) sin (θ) = 1

csc (θ) sin (θ)

用 sin, cos 表示

csc (θ) sin (θ)

使用基本三角恒等式:

csc (θ) = \frac{1}{sin ( θ )}

= \frac{1}{sin ( θ )} sin (θ)

\frac{1}{sin ( θ )} sin (θ) = 1

\frac{1}{sin ( θ )} sin (θ)

分式相乘:

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

= \frac{1 sin ( θ )}{sin ( θ )}

约分:

sin (θ)

= 1

= 1

= cot (θ) - 1

cot (θ) - 1 = 0

将

1

到右边

cot (θ) - 1 = 0

两边加上

1

cot (θ) - 1 + 1 = 0 + 1

化简

cot (θ) = 1

cot (θ) = 1

cot (θ) = 1

的通解

cot (x)

周期表（周期为

πn

）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

θ = \frac{π}{4} + πn

θ = \frac{π}{4} + πn

作图

流行的例子

cos (t) = - \frac{2}{3}

0 = 4 cos (4 x)

tan(θ)= 8/7 ,pi<θ<(3pi)/2

tan (θ) = \frac{8}{7}, π < θ < \frac{3 π}{2}

csc(θ)sin(θ)=cot(θ)

csc (θ) sin (θ) = cot (θ)

tan(θ+pi)+2sin(θ+pi)=0

tan (θ + π) + 2 sin (θ + π) = 0