zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

solvefor a,cos(ax)+(b/x)sin(ax)=0

解答

求解

a, cos (a x) + (\frac{b}{x}) sin (a x) = 0

解答

a = \frac{arctan ( - \frac{x}{b} )}{x} + \frac{πn}{x}

求解步骤

cos (a x) + (\frac{b}{x}) sin (a x) = 0

使用三角恒等式改写

cos (a x) + \frac{b}{x} sin (a x) = 0

在两边除以

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

\frac{cos ( a x ) + \frac{b}{x} sin ( a x )}{cos ( a x )} = \frac{0}{cos ( a x )}

化简

1 + \frac{b sin ( a x )}{x cos ( a x )} = 0

使用基本三角恒等式:

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

1 + \frac{b tan ( a x )}{x} = 0

1 + \frac{b tan ( a x )}{x} = 0

将

1

到右边

1 + \frac{b tan ( a x )}{x} = 0

两边减去

1

1 + \frac{b tan ( a x )}{x} - 1 = 0 - 1

化简

\frac{b tan ( a x )}{x} = - 1

\frac{b tan ( a x )}{x} = - 1

在两边乘以

x

\frac{b tan ( a x )}{x} = - 1

在两边乘以

x

\frac{b tan ( a x ) x}{x} = (- 1) x; x \neq = 0

化简

b tan (a x) = - x; x \neq = 0

b tan (a x) = - x; x \neq = 0

两边除以

b; x \neq = 0, b \neq = 0

b tan (a x) = - x; x \neq = 0

两边除以

b; x \neq = 0, b \neq = 0

\frac{b tan ( a x )}{b} = \frac{- x}{b}; x \neq = 0, b \neq = 0

化简

tan (a x) = - \frac{x}{b}; x \neq = 0, b \neq = 0

tan (a x) = - \frac{x}{b}; x \neq = 0, b \neq = 0

使用反三角函数性质

tan (a x) = - \frac{x}{b}

tan (a x) = - \frac{x}{b}

的通解

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

a x = arctan (- \frac{x}{b}) + πn

a x = arctan (- \frac{x}{b}) + πn

解

a x = arctan (- \frac{x}{b}) + πn : a = \frac{arctan ( - \frac{x}{b} )}{x} + \frac{πn}{x}; x \neq = 0

a x = arctan (- \frac{x}{b}) + πn

两边除以

x; x \neq = 0

a x = arctan (- \frac{x}{b}) + πn

两边除以

x; x \neq = 0

\frac{a x}{x} = \frac{arctan ( - \frac{x}{b} )}{x} + \frac{πn}{x}; x \neq = 0

化简

a = \frac{arctan ( - \frac{x}{b} )}{x} + \frac{πn}{x}; x \neq = 0

a = \frac{arctan ( - \frac{x}{b} )}{x} + \frac{πn}{x}; x \neq = 0

a = \frac{arctan ( - \frac{x}{b} )}{x} + \frac{πn}{x}

作图

流行的例子

cos^4(a)+cos^2(a)+sin^2(a)+sin^2(a)=1

cos^{4} (a) + cos^{2} (a) + sin^{2} (a) + sin^{2} (a) = 1

cos^3(x)-2sin(x)-0.7=0

cos^{3} (x) - 2 sin (x) - 0.7 = 0

solvefor y=cos(x),x

so l v e f or y = cos (x), x

tan(θ)= 5/(5sqrt(3))

tan (θ) = \frac{5}{5 3}

cos (x) = 7