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인기 있는 삼각법 >

solvefor x,sin(x)+cos(y)=sin(x)cos(y)

해법

을 위해 해결하다

x, sin (x) + cos (y) = sin (x) cos (y)

해법

x = arccsc (\frac{cos ( y ) - 1}{cos ( y )}) + 2 πn, x = π + arccsc (- \frac{cos ( y ) - 1}{cos ( y )}) + 2 πn

솔루션 단계

sin (x) + cos (y) = sin (x) cos (y)

빼다

sin (x) cos (y)

양쪽에서

sin (x) + cos (y) - cos (y) sin (x) = 0

삼각성을 사용하여 다시 쓰기

cos (y) + sin (x) - cos (y) sin (x)

기본 삼각형 항등식 사용:

sin (x) = \frac{1}{csc ( x )}

= cos (y) + \frac{1}{csc ( x )} - cos (y) \frac{1}{csc ( x )}

cos (y) + \frac{1}{csc ( x )} - cos (y) \frac{1}{csc ( x )}

간소화하다 :

cos (y) + \frac{1 - cos ( y )}{csc ( x )}

cos (y) + \frac{1}{csc ( x )} - cos (y) \frac{1}{csc ( x )}

cos (y) \frac{1}{csc ( x )} = \frac{cos ( y )}{csc ( x )}

cos (y) \frac{1}{csc ( x )}

다중 분수:

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

= \frac{1 \cdot cos ( y )}{csc ( x )}

곱하다:

1 \cdot cos (y) = cos (y)

= \frac{cos ( y )}{csc ( x )}

= cos (y) + \frac{1}{csc ( x )} - \frac{cos ( y )}{csc ( x )}

분수를 합치다

\frac{1}{csc ( x )} - \frac{cos ( y )}{csc ( x )} : \frac{1 - cos ( y )}{csc ( x )}

규칙 적용

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

= \frac{1 - cos ( y )}{csc ( x )}

= cos (y) + \frac{- cos ( y ) + 1}{csc ( x )}

= cos (y) + \frac{1 - cos ( y )}{csc ( x )}

cos (y) + \frac{1 - cos ( y )}{csc ( x )} = 0

양쪽을 곱한 값

csc (x)

cos (y) + \frac{1 - cos ( y )}{csc ( x )} = 0

양쪽을 곱한 값

csc (x)

cos (y) csc (x) + \frac{1 - cos ( y )}{csc ( x )} csc (x) = 0 \cdot csc (x)

단순화

cos (y) csc (x) + \frac{1 - cos ( y )}{csc ( x )} csc (x) = 0 \cdot csc (x)

\frac{1 - cos ( y )}{csc ( x )} csc (x)

간소화하다 :

1 - cos (y)

\frac{1 - cos ( y )}{csc ( x )} csc (x)

다중 분수:

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

= \frac{( 1 - cos ( y ) ) csc ( x )}{csc ( x )}

공통 요인 취소:

csc (x)

= 1 - cos (y)

0 \cdot csc (x)

간소화하다 :

0

0 \cdot csc (x)

규칙 적용

0 \cdot a = 0

= 0

cos (y) csc (x) + 1 - cos (y) = 0

cos (y) csc (x) + 1 - cos (y) = 0

cos (y) csc (x) + 1 - cos (y) = 0

cos (y)

를 오른쪽으로 이동

cos (y) csc (x) + 1 - cos (y) = 0

더하다

cos (y)

양쪽으로

cos (y) csc (x) + 1 - cos (y) + cos (y) = 0 + cos (y)

단순화

cos (y) csc (x) + 1 = cos (y)

cos (y) csc (x) + 1 = cos (y)

1

를 오른쪽으로 이동

cos (y) csc (x) + 1 = cos (y)

빼다

1

양쪽에서

cos (y) csc (x) + 1 - 1 = cos (y) - 1

단순화

cos (y) csc (x) = cos (y) - 1

cos (y) csc (x) = cos (y) - 1

양쪽을 다음으로 나눕니다

cos (y); y \neq = \frac{π}{2} + 2 πn, y \neq = \frac{3 π}{2} + 2 πn

cos (y) csc (x) = cos (y) - 1

양쪽을 다음으로 나눕니다

cos (y); y \neq = \frac{π}{2} + 2 πn, y \neq = \frac{3 π}{2} + 2 πn

\frac{cos ( y ) csc ( x )}{cos ( y )} = \frac{cos ( y )}{cos ( y )} - \frac{1}{cos ( y )}; y \neq = \frac{π}{2} + 2 πn, y \neq = \frac{3 π}{2} + 2 πn

단순화

\frac{cos ( y ) csc ( x )}{cos ( y )} = \frac{cos ( y )}{cos ( y )} - \frac{1}{cos ( y )}

\frac{cos ( y ) csc ( x )}{cos ( y )}

간소화하다 :

csc (x)

\frac{cos ( y ) csc ( x )}{cos ( y )}

공통 요인 취소:

cos (y)

= csc (x)

\frac{cos ( y )}{cos ( y )} - \frac{1}{cos ( y )}

간소화하다 :

\frac{cos ( y ) - 1}{cos ( y )}

\frac{cos ( y )}{cos ( y )} - \frac{1}{cos ( y )}

규칙 적용

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

= \frac{cos ( y ) - 1}{cos ( y )}

csc (x) = \frac{cos ( y ) - 1}{cos ( y )}; y \neq = \frac{π}{2} + 2 πn, y \neq = \frac{3 π}{2} + 2 πn

csc (x) = \frac{cos ( y ) - 1}{cos ( y )}; y \neq = \frac{π}{2} + 2 πn, y \neq = \frac{3 π}{2} + 2 πn

csc (x) = \frac{cos ( y ) - 1}{cos ( y )}; y \neq = \frac{π}{2} + 2 πn, y \neq = \frac{3 π}{2} + 2 πn

트리거 역속성 적용

csc (x) = \frac{cos ( y ) - 1}{cos ( y )}

일반 솔루션

csc (x) = \frac{cos ( y ) - 1}{cos ( y )}

csc (x) = a \Rightarrow x = arccsc (a) + 2 πn, x = π + arccsc (a) + 2 πn

x = arccsc (\frac{cos ( y ) - 1}{cos ( y )}) + 2 πn, x = π + arccsc (- \frac{cos ( y ) - 1}{cos ( y )}) + 2 πn

x = arccsc (\frac{cos ( y ) - 1}{cos ( y )}) + 2 πn, x = π + arccsc (- \frac{cos ( y ) - 1}{cos ( y )}) + 2 πn

그래프

인기 있는 예

solvefor x,z=arctan(x/y)

so l v e f or x, z = arctan (\frac{x}{y})

- \frac{1}{2} = cos (θ)

4cos^2(x)-3cos(x)-2=0

4 cos^{2} (x) - 3 cos (x) - 2 = 0

sin (x) = cos (3 x)

solvefor x,y=5sin(x/4)

so l v e f or x, y = 5 sin (\frac{x}{4})