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인기 있는 삼각법 >

solvefor x,y=(sec(x))/(cos^1(x))+8y^2

해법

을 위해 해결하다

x, y = \frac{sec ( x )}{cos ^{1} ( x )} + 8 y^{2}

해법

x = arcsec (y - 8 y^{2}) + 2 πn, x = - arcsec (y - 8 y^{2}) + 2 πn, x = arcsec (- y - 8 y^{2}) + 2 πn, x = - arcsec (- y - 8 y^{2}) + 2 πn

솔루션 단계

y = \frac{sec ( x )}{cos ^{1} ( x )} + 8 y^{2}

측면 전환

\frac{sec ( x )}{cos ^{1} ( x )} + 8 y^{2} = y

빼다

y

양쪽에서

\frac{sec ( x )}{cos ( x )} + 8 y^{2} - y = 0

\frac{sec ( x )}{cos ( x )} + 8 y^{2} - y

단순화하세요:

\frac{sec ( x ) + 8 y ^{2} cos ( x ) - y cos ( x )}{cos ( x )}

\frac{sec ( x )}{cos ( x )} + 8 y^{2} - y

요소를 분수로 변환:

8 y^{2} = \frac{8 y ^{2} cos ( x )}{cos ( x )}, y = \frac{y cos ( x )}{cos ( x )}

= \frac{sec ( x )}{cos ( x )} + \frac{8 y ^{2} cos ( x )}{cos ( x )} - \frac{y cos ( x )}{cos ( x )}

분모가 같기 때문에, 분수를 합친다:

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

= \frac{sec ( x ) + 8 y ^{2} cos ( x ) - y cos ( x )}{cos ( x )}

\frac{sec ( x ) + 8 y ^{2} cos ( x ) - y cos ( x )}{cos ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

sec (x) + 8 y^{2} cos (x) - y cos (x) = 0

삼각성을 사용하여 다시 쓰기

sec (x) - cos (x) y + 8 cos (x) y^{2}

기본 삼각형 항등식 사용:

cos (x) = \frac{1}{sec ( x )}

= sec (x) - \frac{1}{sec ( x )} y + 8 \cdot \frac{1}{sec ( x )} y^{2}

sec (x) - \frac{1}{sec ( x )} y + 8 \cdot \frac{1}{sec ( x )} y^{2}

간소화하다 :

sec (x) + \frac{- y + 8 y ^{2}}{sec ( x )}

sec (x) - \frac{1}{sec ( x )} y + 8 \cdot \frac{1}{sec ( x )} y^{2}

\frac{1}{sec ( x )} y = \frac{y}{sec ( x )}

\frac{1}{sec ( x )} y

다중 분수:

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

= \frac{1 \cdot y}{sec ( x )}

곱하다:

1 \cdot y = y

= \frac{y}{sec ( x )}

8 \cdot \frac{1}{sec ( x )} y^{2} = \frac{8 y ^{2}}{sec ( x )}

8 \cdot \frac{1}{sec ( x )} y^{2}

다중 분수:

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

= \frac{1 \cdot 8 y ^{2}}{sec ( x )}

숫자를 곱하시오:

1 \cdot 8 = 8

= \frac{8 y ^{2}}{sec ( x )}

= sec (x) - \frac{y}{sec ( x )} + \frac{8 y ^{2}}{sec ( x )}

분수를 합치다

- \frac{y}{sec ( x )} + \frac{8 y ^{2}}{sec ( x )} : \frac{- y + 8 y ^{2}}{sec ( x )}

규칙 적용

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

= \frac{- y + 8 y ^{2}}{sec ( x )}

= sec (x) + \frac{8 y ^{2} - y}{sec ( x )}

= sec (x) + \frac{- y + 8 y ^{2}}{sec ( x )}

\frac{- y + 8 y ^{2}}{sec ( x )} + sec (x) = 0

대체로 해결

\frac{- y + 8 y ^{2}}{sec ( x )} + sec (x) = 0

하게:

sec (x) = u

\frac{- y + 8 y ^{2}}{u} + u = 0

\frac{- y + 8 y ^{2}}{u} + u = 0 : u = y - 8 y^{2}, u = - y - 8 y^{2}

\frac{- y + 8 y ^{2}}{u} + u = 0

양쪽을 곱한 값

u

\frac{- y + 8 y ^{2}}{u} + u = 0

양쪽을 곱한 값

u

\frac{- y + 8 y ^{2}}{u} u + uu = 0 \cdot u

단순화

\frac{- y + 8 y ^{2}}{u} u + uu = 0 \cdot u

\frac{- y + 8 y ^{2}}{u} u

간소화하다 :

- y + 8 y^{2}

\frac{- y + 8 y ^{2}}{u} u

다중 분수:

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

= \frac{( - y + 8 y ^{2} ) u}{u}

공통 요인 취소:

u

= - - y + 8 y^{2}

uu

간소화하다 :

u^{2}

uu

지수 규칙 적용:

a^{b} \cdot a^{c} = a^{b + c}

uu = u^{1 + 1}

= u^{1 + 1}

숫자 추가:

1 + 1 = 2

= u^{2}

0 \cdot u

간소화하다 :

0

0 \cdot u

규칙 적용

0 \cdot a = 0

= 0

- y + 8 y^{2} + u^{2} = 0

- y + 8 y^{2} + u^{2} = 0

- y + 8 y^{2} + u^{2} = 0

- y + 8 y^{2} + u^{2} = 0

해결 :

u = y - 8 y^{2}, u = - y - 8 y^{2}

- y + 8 y^{2} + u^{2} = 0

y

를 오른쪽으로 이동

- y + 8 y^{2} + u^{2} = 0

더하다

y

양쪽으로

- y + 8 y^{2} + u^{2} + y = 0 + y

단순화

8 y^{2} + u^{2} = y

8 y^{2} + u^{2} = y

8 y^{2}

를 오른쪽으로 이동

8 y^{2} + u^{2} = y

빼다

8 y^{2}

양쪽에서

8 y^{2} + u^{2} - 8 y^{2} = y - 8 y^{2}

단순화

u^{2} = y - 8 y^{2}

u^{2} = y - 8 y^{2}

위해서

x^{2} = f (a)

해결책은

x = f (a), - f (a)

u = y - 8 y^{2}, u = - y - 8 y^{2}

u = y - 8 y^{2}, u = - y - 8 y^{2}

뒤로 대체

u = sec (x)

sec (x) = y - 8 y^{2}, sec (x) = - y - 8 y^{2}

sec (x) = y - 8 y^{2}, sec (x) = - y - 8 y^{2}

sec (x) = y - 8 y^{2} : x = arcsec (y - 8 y^{2}) + 2 πn, x = - arcsec (y - 8 y^{2}) + 2 πn

sec (x) = y - 8 y^{2}

트리거 역속성 적용

sec (x) = y - 8 y^{2}

일반 솔루션

sec (x) = y - 8 y^{2}

sec (x) = a \Rightarrow x = arcsec (a) + 2 πn, x = - arcsec (a) + 2 πn

x = arcsec (y - 8 y^{2}) + 2 πn, x = - arcsec (y - 8 y^{2}) + 2 πn

x = arcsec (y - 8 y^{2}) + 2 πn, x = - arcsec (y - 8 y^{2}) + 2 πn

sec (x) = - y - 8 y^{2} : x = arcsec (- y - 8 y^{2}) + 2 πn, x = - arcsec (- y - 8 y^{2}) + 2 πn

sec (x) = - y - 8 y^{2}

트리거 역속성 적용

sec (x) = - y - 8 y^{2}

일반 솔루션

sec (x) = - y - 8 y^{2}

sec (x) = a \Rightarrow x = arcsec (a) + 2 πn, x = - arcsec (a) + 2 πn

x = arcsec (- y - 8 y^{2}) + 2 πn, x = - arcsec (- y - 8 y^{2}) + 2 πn

x = arcsec (- y - 8 y^{2}) + 2 πn, x = - arcsec (- y - 8 y^{2}) + 2 πn

모든 솔루션 결합

x = arcsec (y - 8 y^{2}) + 2 πn, x = - arcsec (y - 8 y^{2}) + 2 πn, x = arcsec (- y - 8 y^{2}) + 2 πn, x = - arcsec (- y - 8 y^{2}) + 2 πn

그래프

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