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人気のある三角関数 >

solvefor a,F=(x^{(2/3)})+(0.9(3.3-x^2)^{1/2})*sin(apex)

解

解く

a, F = (x^{(\frac{2}{3})}) + (0.9 (3.3 - x^{2})^{\frac{1}{2}}) \cdot sin (a p e x)

解

a = \frac{arcsin ( \frac{F - x ^{\frac{2}{3}}}{0.9 ( - x ^{2} + 3.3 ) ^{\frac{1}{2}}} )}{p e x} + \frac{2 πn}{p e x}, a = \frac{π}{p e x} + \frac{arcsin ( - \frac{F - x ^{\frac{2}{3}}}{0.9 ( - x ^{2} + 3.3 ) ^{\frac{1}{2}}} )}{p e x} + \frac{2 πn}{p e x}

解答ステップ

F = (x^{(\frac{2}{3})}) + (0.9 (3.3 - x^{2})^{\frac{1}{2}}) sin (a p e x)

辺を交換する

x^{\frac{2}{3}} + 0.9 (3.3 - x^{2})^{\frac{1}{2}} sin (a p e x) = F

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

を右側に移動します

x^{\frac{2}{3}} + 0.9 (3.3 - x^{2})^{\frac{1}{2}} sin (a p e x) = F

両辺から

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

を引く

x^{\frac{2}{3}} + 0.9 (3.3 - x^{2})^{\frac{1}{2}} sin (a p e x) - x^{\frac{2}{3}} = F - x^{\frac{2}{3}}

簡素化

0.9 (3.3 - x^{2})^{\frac{1}{2}} sin (a p e x) = F - x^{\frac{2}{3}}

0.9 (3.3 - x^{2})^{\frac{1}{2}} sin (a p e x) = F - x^{\frac{2}{3}}

以下で両辺を割る

0.9 (3.3 - x^{2})^{\frac{1}{2}}; x \neq = \frac{33}{10}, x \neq = - \frac{33}{10}

0.9 (3.3 - x^{2})^{\frac{1}{2}} sin (a p e x) = F - x^{\frac{2}{3}}

以下で両辺を割る

0.9 (3.3 - x^{2})^{\frac{1}{2}}; x \neq = \frac{33}{10}, x \neq = - \frac{33}{10}

\frac{0.9 ( 3.3 - x ^{2} ) ^{\frac{1}{2}} sin ( a p e x )}{0.9 ( 3.3 - x ^{2} ) ^{\frac{1}{2}}} = \frac{F}{0.9 ( 3.3 - x ^{2} ) ^{\frac{1}{2}}} - \frac{x ^{\frac{2}{3}}}{0.9 ( 3.3 - x ^{2} ) ^{\frac{1}{2}}}; x \neq = \frac{33}{10}, x \neq = - \frac{33}{10}

簡素化

\frac{0.9 ( 3.3 - x ^{2} ) ^{\frac{1}{2}} sin ( a p e x )}{0.9 ( 3.3 - x ^{2} ) ^{\frac{1}{2}}} = \frac{F}{0.9 ( 3.3 - x ^{2} ) ^{\frac{1}{2}}} - \frac{x ^{\frac{2}{3}}}{0.9 ( 3.3 - x ^{2} ) ^{\frac{1}{2}}}

簡素化

\frac{0.9 ( 3.3 - x ^{2} ) ^{\frac{1}{2}} sin ( a p e x )}{0.9 ( 3.3 - x ^{2} ) ^{\frac{1}{2}}} : sin (a p e x)

\frac{0.9 ( 3.3 - x ^{2} ) ^{\frac{1}{2}} sin ( a p e x )}{0.9 ( 3.3 - x ^{2} ) ^{\frac{1}{2}}}

共通因数を約分する:

0.9

= \frac{sin ( a p e x ) ( - x ^{2} + 3.3 ) ^{\frac{1}{2}}}{( 3.3 - x ^{2} ) ^{\frac{1}{2}}}

共通因数を約分する:

(3.3 - x^{2})^{\frac{1}{2}}

= sin (a p e x)

簡素化

\frac{F}{0.9 ( 3.3 - x ^{2} ) ^{\frac{1}{2}}} - \frac{x ^{\frac{2}{3}}}{0.9 ( 3.3 - x ^{2} ) ^{\frac{1}{2}}} : \frac{F - x ^{\frac{2}{3}}}{0.9 ( - x ^{2} + 3.3 ) ^{\frac{1}{2}}}

\frac{F}{0.9 ( 3.3 - x ^{2} ) ^{\frac{1}{2}}} - \frac{x ^{\frac{2}{3}}}{0.9 ( 3.3 - x ^{2} ) ^{\frac{1}{2}}}

規則を適用

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

= \frac{F - x ^{\frac{2}{3}}}{0.9 ( - x ^{2} + 3.3 ) ^{\frac{1}{2}}}

sin (a p e x) = \frac{F - x ^{\frac{2}{3}}}{0.9 ( - x ^{2} + 3.3 ) ^{\frac{1}{2}}}; x \neq = \frac{33}{10}, x \neq = - \frac{33}{10}

sin (a p e x) = \frac{F - x ^{\frac{2}{3}}}{0.9 ( - x ^{2} + 3.3 ) ^{\frac{1}{2}}}; x \neq = \frac{33}{10}, x \neq = - \frac{33}{10}

sin (a p e x) = \frac{F - x ^{\frac{2}{3}}}{0.9 ( - x ^{2} + 3.3 ) ^{\frac{1}{2}}}; x \neq = \frac{33}{10}, x \neq = - \frac{33}{10}

三角関数の逆数プロパティを適用する

sin (a p e x) = \frac{F - x ^{\frac{2}{3}}}{0.9 ( - x ^{2} + 3.3 ) ^{\frac{1}{2}}}

以下の一般解

sin (a p e x) = \frac{F - x ^{\frac{2}{3}}}{0.9 ( - x ^{2} + 3.3 ) ^{\frac{1}{2}}}

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

a p e x = arcsin (\frac{F - x ^{\frac{2}{3}}}{0.9 ( - x ^{2} + 3.3 ) ^{\frac{1}{2}}}) + 2 πn, a p e x = π + arcsin (- \frac{F - x ^{\frac{2}{3}}}{0.9 ( - x ^{2} + 3.3 ) ^{\frac{1}{2}}}) + 2 πn

a p e x = arcsin (\frac{F - x ^{\frac{2}{3}}}{0.9 ( - x ^{2} + 3.3 ) ^{\frac{1}{2}}}) + 2 πn, a p e x = π + arcsin (- \frac{F - x ^{\frac{2}{3}}}{0.9 ( - x ^{2} + 3.3 ) ^{\frac{1}{2}}}) + 2 πn

解く

a p e x = arcsin (\frac{F - x ^{\frac{2}{3}}}{0.9 ( - x ^{2} + 3.3 ) ^{\frac{1}{2}}}) + 2 πn : a = \frac{arcsin ( \frac{F - x ^{\frac{2}{3}}}{0.9 ( - x ^{2} + 3.3 ) ^{\frac{1}{2}}} )}{p e x} + \frac{2 πn}{p e x}; p e x \neq = 0

a p e x = arcsin (\frac{F - x ^{\frac{2}{3}}}{0.9 ( - x ^{2} + 3.3 ) ^{\frac{1}{2}}}) + 2 πn

以下で両辺を割る

p e x; p e x \neq = 0

a p e x = arcsin (\frac{F - x ^{\frac{2}{3}}}{0.9 ( - x ^{2} + 3.3 ) ^{\frac{1}{2}}}) + 2 πn

以下で両辺を割る

p e x; p e x \neq = 0

\frac{a p e x}{p e x} = \frac{arcsin ( \frac{F - x ^{\frac{2}{3}}}{0.9 ( - x ^{2} + 3.3 ) ^{\frac{1}{2}}} )}{p e x} + \frac{2 πn}{p e x}; p e x \neq = 0

簡素化

a = \frac{arcsin ( \frac{F - x ^{\frac{2}{3}}}{0.9 ( - x ^{2} + 3.3 ) ^{\frac{1}{2}}} )}{p e x} + \frac{2 πn}{p e x}; p e x \neq = 0

a = \frac{arcsin ( \frac{F - x ^{\frac{2}{3}}}{0.9 ( - x ^{2} + 3.3 ) ^{\frac{1}{2}}} )}{p e x} + \frac{2 πn}{p e x}; p e x \neq = 0

解く

a p e x = π + arcsin (- \frac{F - x ^{\frac{2}{3}}}{0.9 ( - x ^{2} + 3.3 ) ^{\frac{1}{2}}}) + 2 πn : a = \frac{π}{p e x} + \frac{arcsin ( - \frac{F - x ^{\frac{2}{3}}}{0.9 ( - x ^{2} + 3.3 ) ^{\frac{1}{2}}} )}{p e x} + \frac{2 πn}{p e x}; p e x \neq = 0

a p e x = π + arcsin (- \frac{F - x ^{\frac{2}{3}}}{0.9 ( - x ^{2} + 3.3 ) ^{\frac{1}{2}}}) + 2 πn

以下で両辺を割る

p e x; p e x \neq = 0

a p e x = π + arcsin (- \frac{F - x ^{\frac{2}{3}}}{0.9 ( - x ^{2} + 3.3 ) ^{\frac{1}{2}}}) + 2 πn

以下で両辺を割る

p e x; p e x \neq = 0

\frac{a p e x}{p e x} = \frac{π}{p e x} + \frac{arcsin ( - \frac{F - x ^{\frac{2}{3}}}{0.9 ( - x ^{2} + 3.3 ) ^{\frac{1}{2}}} )}{p e x} + \frac{2 πn}{p e x}; p e x \neq = 0

簡素化

a = \frac{π}{p e x} + \frac{arcsin ( - \frac{F - x ^{\frac{2}{3}}}{0.9 ( - x ^{2} + 3.3 ) ^{\frac{1}{2}}} )}{p e x} + \frac{2 πn}{p e x}; p e x \neq = 0

a = \frac{π}{p e x} + \frac{arcsin ( - \frac{F - x ^{\frac{2}{3}}}{0.9 ( - x ^{2} + 3.3 ) ^{\frac{1}{2}}} )}{p e x} + \frac{2 πn}{p e x}; p e x \neq = 0

a = \frac{arcsin ( \frac{F - x ^{\frac{2}{3}}}{0.9 ( - x ^{2} + 3.3 ) ^{\frac{1}{2}}} )}{p e x} + \frac{2 πn}{p e x}, a = \frac{π}{p e x} + \frac{arcsin ( - \frac{F - x ^{\frac{2}{3}}}{0.9 ( - x ^{2} + 3.3 ) ^{\frac{1}{2}}} )}{p e x} + \frac{2 πn}{p e x}

グラフ

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