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受欢迎的三角函数 >

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

解答

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

解答

x = 0.33983 \dots + 2 πn, x = π - 0.33983 \dots + 2 πn

+1

度数

x = 19.47122 \dots^{\circ} + 36 0^{\circ} n, x = 160.52877 \dots^{\circ} + 36 0^{\circ} n

求解步骤

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

两边减去

\frac{1}{cos ( x )}

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

化简

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

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

将项转换为分式:

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

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

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

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

3 tan (x) cos (x) - 1 = 0

使用三角恒等式改写

3 tan (x) cos (x) - 1

cos (x) tan (x) = sin (x)

cos (x) tan (x)

使用基本三角恒等式:

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

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

化简

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

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

分式相乘:

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

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

约分:

cos (x)

= sin (x)

= sin (x)

= - 1 + 3 sin (x)

- 1 + 3 sin (x) = 0

将

1

到右边

- 1 + 3 sin (x) = 0

两边加上

1

- 1 + 3 sin (x) + 1 = 0 + 1

化简

3 sin (x) = 1

3 sin (x) = 1

两边除以

3

3 sin (x) = 1

两边除以

3

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

化简

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

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

使用反三角函数性质

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

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

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (\frac{1}{3}) + 2 πn, x = π - arcsin (\frac{1}{3}) + 2 πn

x = arcsin (\frac{1}{3}) + 2 πn, x = π - arcsin (\frac{1}{3}) + 2 πn

以小数形式表示解

x = 0.33983 \dots + 2 πn, x = π - 0.33983 \dots + 2 πn

作图

流行的例子

cos(x)-sin(x)=0,-pi<= x<= pi

cos (x) - sin (x) = 0, - π \leq x \leq π

5 - tan^{2} (x) = 4

2sec^2(θ)-3=tan^2(θ)

2 sec^{2} (θ) - 3 = tan^{2} (θ)

sin(pi-x)+cos(x)=0

sin (π - x) + cos (x) = 0

sin(x)=-sin(2x)

sin (x) = - sin (2 x)