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شائع علم المثلثات >

solvefor k,f=x^{2/3}+(10-x^2)^{0.5}sin(kpix)

الحلّ

solve for

k, f = x^{\frac{2}{3}} + (10 - x^{2})^{0.5} sin (kπ x)

الحلّ

k = \frac{arcsin ( \frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}} )}{π x} + \frac{2 n}{x}, k = \frac{1}{x} + \frac{arcsin ( - \frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}} )}{π x} + \frac{2 n}{x}

خطوات الحلّ

f = x^{\frac{2}{3}} + (10 - x^{2})^{0.5} sin (kπ x)

بدّل الأطراف

x^{\frac{2}{3}} + (10 - x^{2})^{0.5} sin (kπ x) = f

انقل

x^{\frac{2}{3}}

إلى الجانب الأيمن

x^{\frac{2}{3}} + (10 - x^{2})^{0.5} sin (kπ x) = f

من الطرفين

x^{\frac{2}{3}}

اطرح

x^{\frac{2}{3}} + (10 - x^{2})^{0.5} sin (kπ x) - x^{\frac{2}{3}} = f - x^{\frac{2}{3}}

بسّط

(10 - x^{2})^{0.5} sin (kπ x) = f - x^{\frac{2}{3}}

(10 - x^{2})^{0.5} sin (kπ x) = f - x^{\frac{2}{3}}

(10 - x^{2})^{0.5}; x \neq = 10, x \neq = - 10

اقسم الطرفين على

(10 - x^{2})^{0.5} sin (kπ x) = f - x^{\frac{2}{3}}

(10 - x^{2})^{0.5}; x \neq = 10, x \neq = - 10

اقسم الطرفين على

\frac{( 10 - x ^{2} ) ^{0.5} sin ( kπ x )}{( 10 - x ^{2} ) ^{0.5}} = \frac{f}{( 10 - x ^{2} ) ^{0.5}} - \frac{x ^{\frac{2}{3}}}{( 10 - x ^{2} ) ^{0.5}}; x \neq = 10, x \neq = - 10

بسّط

\frac{( 10 - x ^{2} ) ^{0.5} sin ( kπ x )}{( 10 - x ^{2} ) ^{0.5}} = \frac{f}{( 10 - x ^{2} ) ^{0.5}} - \frac{x ^{\frac{2}{3}}}{( 10 - x ^{2} ) ^{0.5}}

\frac{( 10 - x ^{2} ) ^{\frac{1}{2}} sin ( kπ x )}{( 10 - x ^{2} ) ^{\frac{1}{2}}}

بسّط:

sin (kπ x)

\frac{( 10 - x ^{2} ) ^{0.5} sin ( kπ x )}{( 10 - x ^{2} ) ^{0.5}}

(10 - x^{2})^{\frac{1}{2}} :

إلغ العوامل المشتركة

= sin (kπ x)

\frac{f}{( 10 - x ^{2} ) ^{\frac{1}{2}}} - \frac{x ^{\frac{2}{3}}}{( 10 - x ^{2} ) ^{\frac{1}{2}}}

بسّط:

\frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}}

\frac{f}{( 10 - x ^{2} ) ^{0.5}} - \frac{x ^{\frac{2}{3}}}{( 10 - x ^{2} ) ^{0.5}}

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

فعّل القانون

= \frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}}

sin (kπ x) = \frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}}; x \neq = 10, x \neq = - 10

sin (kπ x) = \frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}}; x \neq = 10, x \neq = - 10

sin (kπ x) = \frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}}; x \neq = 10, x \neq = - 10

Apply trig inverse properties

sin (kπ x) = \frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}}

sin (kπ x) = \frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}} :

حلول عامّة لـ

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

kπ x = arcsin (\frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}}) + 2 πn, kπ x = π + arcsin (- \frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}}) + 2 πn

kπ x = arcsin (\frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}}) + 2 πn, kπ x = π + arcsin (- \frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}}) + 2 πn

kπ x = arcsin (\frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}}) + 2 πn

حلّ:

k = \frac{arcsin ( \frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}} )}{π x} + \frac{2 n}{x}; x \neq = 0

kπ x = arcsin (\frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}}) + 2 πn

π x; x \neq = 0

اقسم الطرفين على

kπ x = arcsin (\frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}}) + 2 πn

π x; x \neq = 0

اقسم الطرفين على

\frac{kπ x}{π x} = \frac{arcsin ( \frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}} )}{π x} + \frac{2 πn}{π x}; x \neq = 0

بسّط

k = \frac{arcsin ( \frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}} )}{π x} + \frac{2 n}{x}; x \neq = 0

k = \frac{arcsin ( \frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}} )}{π x} + \frac{2 n}{x}; x \neq = 0

kπ x = π + arcsin (- \frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}}) + 2 πn

حلّ:

k = \frac{1}{x} + \frac{arcsin ( - \frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}} )}{π x} + \frac{2 n}{x}; x \neq = 0

kπ x = π + arcsin (- \frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}}) + 2 πn

π x; x \neq = 0

اقسم الطرفين على

kπ x = π + arcsin (- \frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}}) + 2 πn

π x; x \neq = 0

اقسم الطرفين على

\frac{kπ x}{π x} = \frac{π}{π x} + \frac{arcsin ( - \frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}} )}{π x} + \frac{2 πn}{π x}; x \neq = 0

بسّط

\frac{kπ x}{π x} = \frac{π}{π x} + \frac{arcsin ( - \frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}} )}{π x} + \frac{2 πn}{π x}

\frac{kπ x}{π x}

بسّط:

k

\frac{kπ x}{π x}

π :

إلغ العوامل المشتركة

= \frac{k x}{x}

x :

إلغ العوامل المشتركة

= k

\frac{π}{π x} + \frac{arcsin ( - \frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}} )}{π x} + \frac{2 πn}{π x}

بسّط:

\frac{1}{x} + \frac{arcsin ( - \frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}} )}{π x} + \frac{2 n}{x}

\frac{π}{π x} + \frac{arcsin ( - \frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}} )}{π x} + \frac{2 πn}{π x}

\frac{π}{π x}

اختزل:

\frac{1}{x}

\frac{π}{π x}

π :

إلغ العوامل المشتركة

= \frac{1}{x}

= \frac{1}{x} + \frac{arcsin ( - \frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}} )}{π x} + \frac{2 πn}{π x}

\frac{2 πn}{π x}

اختزل:

\frac{2 n}{x}

\frac{2 πn}{π x}

π :

إلغ العوامل المشتركة

= \frac{2 n}{x}

= \frac{1}{x} + \frac{arcsin ( - \frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}} )}{π x} + \frac{2 n}{x}

k = \frac{1}{x} + \frac{arcsin ( - \frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}} )}{π x} + \frac{2 n}{x}; x \neq = 0

k = \frac{1}{x} + \frac{arcsin ( - \frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}} )}{π x} + \frac{2 n}{x}; x \neq = 0

k = \frac{1}{x} + \frac{arcsin ( - \frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}} )}{π x} + \frac{2 n}{x}; x \neq = 0

k = \frac{arcsin ( \frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}} )}{π x} + \frac{2 n}{x}, k = \frac{1}{x} + \frac{arcsin ( - \frac{f - x ^{\frac{2}{3}}}{( - x ^{2} + 10 ) ^{\frac{1}{2}}} )}{π x} + \frac{2 n}{x}

رسم

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