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인기 있는 삼각법 >

solvefor x,cos(x^3y^3)=5y^3

해법

을 위해 해결하다

x, cos (x^{3} y^{3}) = 5 y^{3}

해법

x = \frac{3 arccos ( 5 y ^{3} ) + 2 πn}{y}, x = \frac{3 - arccos ( 5 y ^{3} ) + 2 πn}{y}

솔루션 단계

cos (x^{3} y^{3}) = 5 y^{3}

트리거 역속성 적용

cos (x^{3} y^{3}) = 5 y^{3}

일반 솔루션

cos (x^{3} y^{3}) = 5 y^{3}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = - arccos (a) + 2 πn

x^{3} y^{3} = arccos (5 y^{3}) + 2 πn, x^{3} y^{3} = - arccos (5 y^{3}) + 2 πn

x^{3} y^{3} = arccos (5 y^{3}) + 2 πn, x^{3} y^{3} = - arccos (5 y^{3}) + 2 πn

x^{3} y^{3} = arccos (5 y^{3}) + 2 πn

해결 :

x = \frac{3 arccos ( 5 y ^{3} ) + 2 πn}{y}; y \neq = 0

x^{3} y^{3} = arccos (5 y^{3}) + 2 πn

양쪽을 다음으로 나눕니다

y^{3}; y \neq = 0

x^{3} y^{3} = arccos (5 y^{3}) + 2 πn

양쪽을 다음으로 나눕니다

y^{3}; y \neq = 0

\frac{x ^{3} y ^{3}}{y ^{3}} = \frac{arccos ( 5 y ^{3} )}{y ^{3}} + \frac{2 πn}{y ^{3}}; y \neq = 0

단순화

x^{3} = \frac{arccos ( 5 y ^{3} )}{y ^{3}} + \frac{2 πn}{y ^{3}}; y \neq = 0

x^{3} = \frac{arccos ( 5 y ^{3} )}{y ^{3}} + \frac{2 πn}{y ^{3}}; y \neq = 0

위해서

x^{n} = f (a)

, n은 이상하다, 해결책은

x = n f (a)

x = 3 \frac{arccos ( 5 y ^{3} )}{y ^{3}} + \frac{2 πn}{y ^{3}}; y \neq = 0

3 \frac{arccos ( 5 y ^{3} )}{y ^{3}} + \frac{2 πn}{y ^{3}}

단순화하세요:

\frac{3 arccos ( 5 y ^{3} ) + 2 πn}{y}

3 \frac{arccos ( 5 y ^{3} )}{y ^{3}} + \frac{2 πn}{y ^{3}}

분수를 합치다

\frac{arccos ( 5 y ^{3} )}{y ^{3}} + \frac{2 πn}{y ^{3}} : \frac{arccos ( 5 y ^{3} ) + 2 πn}{y ^{3}}

규칙 적용

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

= \frac{arccos ( 5 y ^{3} ) + 2 πn}{y ^{3}}

= 3 \frac{arccos ( 5 y ^{3} ) + 2 πn}{y ^{3}}

급진적인 규칙 적용:

n \frac{a}{b} = \frac{n a}{n b},

라면

a \geq 0, b \geq 0

= \frac{3 arccos ( 5 y ^{3} ) + 2 πn}{3 y ^{3}}

급진적인 규칙 적용:

n a^{n} = a,

라면

a \geq 0

3 y^{3} = y

= \frac{3 arccos ( 5 y ^{3} ) + 2 πn}{y}

x = \frac{3 arccos ( 5 y ^{3} ) + 2 πn}{y}; y \neq = 0

x^{3} y^{3} = - arccos (5 y^{3}) + 2 πn

해결 :

x = \frac{3 - arccos ( 5 y ^{3} ) + 2 πn}{y}; y \neq = 0

x^{3} y^{3} = - arccos (5 y^{3}) + 2 πn

양쪽을 다음으로 나눕니다

y^{3}; y \neq = 0

x^{3} y^{3} = - arccos (5 y^{3}) + 2 πn

양쪽을 다음으로 나눕니다

y^{3}; y \neq = 0

\frac{x ^{3} y ^{3}}{y ^{3}} = - \frac{arccos ( 5 y ^{3} )}{y ^{3}} + \frac{2 πn}{y ^{3}}; y \neq = 0

단순화

x^{3} = - \frac{arccos ( 5 y ^{3} )}{y ^{3}} + \frac{2 πn}{y ^{3}}; y \neq = 0

x^{3} = - \frac{arccos ( 5 y ^{3} )}{y ^{3}} + \frac{2 πn}{y ^{3}}; y \neq = 0

위해서

x^{n} = f (a)

, n은 이상하다, 해결책은

x = n f (a)

x = 3 - \frac{arccos ( 5 y ^{3} )}{y ^{3}} + \frac{2 πn}{y ^{3}}; y \neq = 0

3 - \frac{arccos ( 5 y ^{3} )}{y ^{3}} + \frac{2 πn}{y ^{3}}

단순화하세요:

\frac{3 - arccos ( 5 y ^{3} ) + 2 πn}{y}

3 - \frac{arccos ( 5 y ^{3} )}{y ^{3}} + \frac{2 πn}{y ^{3}}

분수를 합치다

- \frac{arccos ( 5 y ^{3} )}{y ^{3}} + \frac{2 πn}{y ^{3}} : \frac{- arccos ( 5 y ^{3} ) + 2 πn}{y ^{3}}

규칙 적용

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

= \frac{- arccos ( 5 y ^{3} ) + 2 πn}{y ^{3}}

= 3 \frac{- arccos ( 5 y ^{3} ) + 2 πn}{y ^{3}}

급진적인 규칙 적용:

n \frac{a}{b} = \frac{n a}{n b},

라면

a \geq 0, b \geq 0

= \frac{3 - arccos ( 5 y ^{3} ) + 2 πn}{3 y ^{3}}

급진적인 규칙 적용:

n a^{n} = a,

라면

a \geq 0

3 y^{3} = y

= \frac{3 - arccos ( 5 y ^{3} ) + 2 πn}{y}

x = \frac{3 - arccos ( 5 y ^{3} ) + 2 πn}{y}; y \neq = 0

x = \frac{3 arccos ( 5 y ^{3} ) + 2 πn}{y}, x = \frac{3 - arccos ( 5 y ^{3} ) + 2 πn}{y}

그래프

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