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受欢迎的三角函数 >

3/(sin(x))= 1/(cos(x))

解答

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

解答

x = 1.24904 \dots + πn

+1

度数

x = 71.56505 \dots^{\circ} + 18 0^{\circ} n

求解步骤

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

两边减去

\frac{1}{cos ( x )}

\frac{3}{sin ( x )} - \frac{1}{cos ( x )} = 0

化简

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

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

sin (x), cos (x)

的最小公倍数:

sin (x) cos (x)

sin (x), cos (x)

最小公倍数 (LCM)

计算出由出现在

sin (x)

或

cos (x)

中的因子组成的表达式

= sin (x) cos (x)

根据最小公倍数调整分式

将每个分子乘以其分母转变为最小公倍数所要乘以的同一数值

sin (x) cos (x)

对于

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

将分母和分子乘以

cos (x)

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

对于

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

将分母和分子乘以

sin (x)

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

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

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

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

3 cos (x) - sin (x) = 0

使用三角恒等式改写

3 cos (x) - sin (x) = 0

在两边除以

cos (x), cos (x) \neq = 0

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

化简

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

使用基本三角恒等式:

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

3 - tan (x) = 0

3 - tan (x) = 0

将

3

到右边

3 - tan (x) = 0

两边减去

3

3 - tan (x) - 3 = 0 - 3

化简

- tan (x) = - 3

- tan (x) = - 3

两边除以

- 1

- tan (x) = - 3

两边除以

- 1

\frac{- tan ( x )}{- 1} = \frac{- 3}{- 1}

化简

tan (x) = 3

tan (x) = 3

使用反三角函数性质

tan (x) = 3

tan (x) = 3

的通解

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan (3) + πn

x = arctan (3) + πn

以小数形式表示解

x = 1.24904 \dots + πn

作图

流行的例子

2cos(t)-2sin(2t)=0

2 cos (t) - 2 sin (2 t) = 0

4sin(x)=-2cos(x)

4 sin (x) = - 2 cos (x)

3 sin (2 x) = 1.5

sin(2x-50)=-1/2

sin (2 x - 5 0^{\circ}) = - \frac{1}{2}

cos(x)=cos(3*x)+2*sin(2*x)

cos (x) = cos (3 \cdot x) + 2 \cdot sin (2 \cdot x)