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شائع علم المثلثات >

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

الحلّ

solve for

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

الحلّ

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

خطوات الحلّ

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

Rewrite using trig identities

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

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

اقسم الطرفين على

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

بسّط

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

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

:Use the basic trigonometric identity

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

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

انقل

1

إلى الجانب الأيمن

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

من الطرفين

1

اطرح

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

بسّط

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

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

x

اضرب الطرفين بـ

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

x

اضرب الطرفين بـ

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

بسّط

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

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

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

اقسم الطرفين على

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

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

اقسم الطرفين على

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

بسّط

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

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

Apply trig inverse properties

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

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

حلول عامّة لـ

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

a x = arctan (- \frac{x}{b}) + πn

a x = arctan (- \frac{x}{b}) + πn

a x = arctan (- \frac{x}{b}) + πn

حلّ:

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

a x = arctan (- \frac{x}{b}) + πn

x; x \neq = 0

اقسم الطرفين على

a x = arctan (- \frac{x}{b}) + πn

x; x \neq = 0

اقسم الطرفين على

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

بسّط

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}

رسم

أمثلة شائعة

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