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인기 있는 삼각법 >

189.4=100tan^2(45-x/2)

해법

189.4 = 100 tan^{2} (4 5^{\circ} - \frac{x}{2})

해법

x = - 36 0^{\circ} n + 9 0^{\circ} - 2 \cdot 0.94242 \dots, x = - 36 0^{\circ} n + 9 0^{\circ} + 2 \cdot 0.94242 \dots

+1

라디안

x = \frac{π}{2} - 2 \cdot 0.94242 \dots - 2 πn, x = \frac{π}{2} + 2 \cdot 0.94242 \dots - 2 πn

솔루션 단계

189.4 = 100 tan^{2} (4 5^{\circ} - \frac{x}{2})

측면 전환

100 tan^{2} (4 5^{\circ} - \frac{x}{2}) = 189.4

대체로 해결

100 tan^{2} (4 5^{\circ} - \frac{x}{2}) = 189.4

하게:

tan (4 5^{\circ} - \frac{x}{2}) = u

100 u^{2} = 189.4

100 u^{2} = 189.4 : u = 1.894, u = - 1.894

100 u^{2} = 189.4

양쪽을 다음으로 나눕니다

100

100 u^{2} = 189.4

양쪽을 다음으로 나눕니다

100

\frac{100 u ^{2}}{100} = \frac{189.4}{100}

단순화

u^{2} = 1.894

u^{2} = 1.894

위해서

x^{2} = f (a)

해결책은

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

u = 1.894, u = - 1.894

뒤로 대체

u = tan (4 5^{\circ} - \frac{x}{2})

tan (4 5^{\circ} - \frac{x}{2}) = 1.894, tan (4 5^{\circ} - \frac{x}{2}) = - 1.894

tan (4 5^{\circ} - \frac{x}{2}) = 1.894, tan (4 5^{\circ} - \frac{x}{2}) = - 1.894

tan (4 5^{\circ} - \frac{x}{2}) = 1.894 : x = - 36 0^{\circ} n + 9 0^{\circ} - 2 arctan (1.894)

tan (4 5^{\circ} - \frac{x}{2}) = 1.894

트리거 역속성 적용

tan (4 5^{\circ} - \frac{x}{2}) = 1.894

일반 솔루션

tan (4 5^{\circ} - \frac{x}{2}) = 1.894

tan (x) = a \Rightarrow x = arctan (a) + 18 0^{\circ} n

4 5^{\circ} - \frac{x}{2} = arctan (1.894) + 18 0^{\circ} n

4 5^{\circ} - \frac{x}{2} = arctan (1.894) + 18 0^{\circ} n

4 5^{\circ} - \frac{x}{2} = arctan (1.894) + 18 0^{\circ} n

해결 :

x = - 36 0^{\circ} n + 9 0^{\circ} - 2 arctan (1.894)

4 5^{\circ} - \frac{x}{2} = arctan (1.894) + 18 0^{\circ} n

4 5^{\circ}

를 오른쪽으로 이동

4 5^{\circ} - \frac{x}{2} = arctan (1.894) + 18 0^{\circ} n

빼다

4 5^{\circ}

양쪽에서

4 5^{\circ} - \frac{x}{2} - 4 5^{\circ} = arctan (1.894) + 18 0^{\circ} n - 4 5^{\circ}

단순화

- \frac{x}{2} = arctan (1.894) + 18 0^{\circ} n - 4 5^{\circ}

- \frac{x}{2} = arctan (1.894) + 18 0^{\circ} n - 4 5^{\circ}

양쪽을 곱한 값

2

- \frac{x}{2} = arctan (1.894) + 18 0^{\circ} n - 4 5^{\circ}

양쪽을 곱한 값

2

2 (- \frac{x}{2}) = 2 arctan (1.894) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

단순화

2 (- \frac{x}{2}) = 2 arctan (1.894) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

2 (- \frac{x}{2})

간소화하다 :

- x

2 (- \frac{x}{2})

괄호 제거:

(- a) = - a

= - 2 \cdot \frac{x}{2}

다중 분수:

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

= - \frac{x \cdot 2}{2}

공통 요인 취소:

2

= - x

2 arctan (1.894) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

간소화하다 :

2 arctan (1.894) + 36 0^{\circ} n - 9 0^{\circ}

2 arctan (1.894) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

2 \cdot 4 5^{\circ} = 9 0^{\circ}

2 \cdot 4 5^{\circ}

다중 분수:

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

= 9 0^{\circ}

공통 요인 취소:

2

= 9 0^{\circ}

= 2 arctan (1.894) + 36 0^{\circ} n - 9 0^{\circ}

- x = 2 arctan (1.894) + 36 0^{\circ} n - 9 0^{\circ}

- x = 2 arctan (1.894) + 36 0^{\circ} n - 9 0^{\circ}

- x = 2 arctan (1.894) + 36 0^{\circ} n - 9 0^{\circ}

양쪽을 다음으로 나눕니다

- 1

- x = 2 arctan (1.894) + 36 0^{\circ} n - 9 0^{\circ}

양쪽을 다음으로 나눕니다

- 1

\frac{- x}{- 1} = \frac{2 arctan ( 1.894 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

단순화

\frac{- x}{- 1} = \frac{2 arctan ( 1.894 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

\frac{- x}{- 1}

간소화하다 :

x

\frac{- x}{- 1}

분수 규칙 적용:

\frac{- a}{- b} = \frac{a}{b}

= \frac{x}{1}

규칙 적용

\frac{a}{1} = a

= x

\frac{2 arctan ( 1.894 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

간소화하다 :

- 36 0^{\circ} n + 9 0^{\circ} - 2 arctan (1.894)

\frac{2 arctan ( 1.894 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

집단적 용어

= \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1} + \frac{2 arctan ( 1.894 )}{- 1}

\frac{36 0 ^{\circ} n}{- 1} = - 36 0^{\circ} n

\frac{36 0 ^{\circ} n}{- 1}

분수 규칙 적용:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{36 0 ^{\circ} n}{1}

규칙 적용

\frac{a}{1} = a

= - 36 0^{\circ} n

= - 36 0^{\circ} n - \frac{9 0 ^{\circ}}{- 1} + \frac{2 arctan ( 1.894 )}{- 1}

\frac{9 0 ^{\circ}}{- 1} = - 9 0^{\circ}

\frac{9 0 ^{\circ}}{- 1}

분수 규칙 적용:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{9 0 ^{\circ}}{1}

분수 규칙 적용:

\frac{a}{1} = a

\frac{9 0 ^{\circ}}{1} = 9 0^{\circ}

= - 9 0^{\circ}

\frac{2 arctan ( 1.894 )}{- 1} = - 2 arctan (1.894)

\frac{2 arctan ( 1.894 )}{- 1}

분수 규칙 적용:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{2 arctan ( 1.894 )}{1}

규칙 적용

\frac{a}{1} = a

= - 2 arctan (1.894)

= - 36 0^{\circ} n - (- 9 0^{\circ}) - 2 arctan (1.894)

규칙 적용

- (- a) = a

= - 36 0^{\circ} n + 9 0^{\circ} - 2 arctan (1.894)

x = - 36 0^{\circ} n + 9 0^{\circ} - 2 arctan (1.894)

x = - 36 0^{\circ} n + 9 0^{\circ} - 2 arctan (1.894)

x = - 36 0^{\circ} n + 9 0^{\circ} - 2 arctan (1.894)

x = - 36 0^{\circ} n + 9 0^{\circ} - 2 arctan (1.894)

tan (4 5^{\circ} - \frac{x}{2}) = - 1.894 : x = - 36 0^{\circ} n + 9 0^{\circ} + 2 arctan (1.894)

tan (4 5^{\circ} - \frac{x}{2}) = - 1.894

트리거 역속성 적용

tan (4 5^{\circ} - \frac{x}{2}) = - 1.894

일반 솔루션

tan (4 5^{\circ} - \frac{x}{2}) = - 1.894

tan (x) = - a \Rightarrow x = arctan (- a) + 18 0^{\circ} n

4 5^{\circ} - \frac{x}{2} = arctan (- 1.894) + 18 0^{\circ} n

4 5^{\circ} - \frac{x}{2} = arctan (- 1.894) + 18 0^{\circ} n

4 5^{\circ} - \frac{x}{2} = arctan (- 1.894) + 18 0^{\circ} n

해결 :

x = - 36 0^{\circ} n + 9 0^{\circ} + 2 arctan (1.894)

4 5^{\circ} - \frac{x}{2} = arctan (- 1.894) + 18 0^{\circ} n

arctan (- 1.894) + 18 0^{\circ} n

간소화하다 :

- arctan (1.894) + 18 0^{\circ} n

arctan (- 1.894) + 18 0^{\circ} n

다음 속성을 사용하십시오:

arctan (- x) = - arctan (x)

arctan (- 1.894) = - arctan (1.894)

= - arctan (1.894) + 18 0^{\circ} n

4 5^{\circ} - \frac{x}{2} = - arctan (1.894) + 18 0^{\circ} n

4 5^{\circ}

를 오른쪽으로 이동

4 5^{\circ} - \frac{x}{2} = - arctan (1.894) + 18 0^{\circ} n

빼다

4 5^{\circ}

양쪽에서

4 5^{\circ} - \frac{x}{2} - 4 5^{\circ} = - arctan (1.894) + 18 0^{\circ} n - 4 5^{\circ}

단순화

- \frac{x}{2} = - arctan (1.894) + 18 0^{\circ} n - 4 5^{\circ}

- \frac{x}{2} = - arctan (1.894) + 18 0^{\circ} n - 4 5^{\circ}

양쪽을 곱한 값

2

- \frac{x}{2} = - arctan (1.894) + 18 0^{\circ} n - 4 5^{\circ}

양쪽을 곱한 값

2

2 (- \frac{x}{2}) = - 2 arctan (1.894) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

단순화

2 (- \frac{x}{2}) = - 2 arctan (1.894) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

2 (- \frac{x}{2})

간소화하다 :

- x

2 (- \frac{x}{2})

괄호 제거:

(- a) = - a

= - 2 \cdot \frac{x}{2}

다중 분수:

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

= - \frac{x \cdot 2}{2}

공통 요인 취소:

2

= - x

- 2 arctan (1.894) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

간소화하다 :

- 2 arctan (1.894) + 36 0^{\circ} n - 9 0^{\circ}

- 2 arctan (1.894) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

2 \cdot 4 5^{\circ} = 9 0^{\circ}

2 \cdot 4 5^{\circ}

다중 분수:

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

= 9 0^{\circ}

공통 요인 취소:

2

= 9 0^{\circ}

= - 2 arctan (1.894) + 36 0^{\circ} n - 9 0^{\circ}

- x = - 2 arctan (1.894) + 36 0^{\circ} n - 9 0^{\circ}

- x = - 2 arctan (1.894) + 36 0^{\circ} n - 9 0^{\circ}

- x = - 2 arctan (1.894) + 36 0^{\circ} n - 9 0^{\circ}

양쪽을 다음으로 나눕니다

- 1

- x = - 2 arctan (1.894) + 36 0^{\circ} n - 9 0^{\circ}

양쪽을 다음으로 나눕니다

- 1

\frac{- x}{- 1} = - \frac{2 arctan ( 1.894 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

단순화

\frac{- x}{- 1} = - \frac{2 arctan ( 1.894 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

\frac{- x}{- 1}

간소화하다 :

x

\frac{- x}{- 1}

분수 규칙 적용:

\frac{- a}{- b} = \frac{a}{b}

= \frac{x}{1}

규칙 적용

\frac{a}{1} = a

= x

- \frac{2 arctan ( 1.894 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

간소화하다 :

- 36 0^{\circ} n + 9 0^{\circ} + 2 arctan (1.894)

- \frac{2 arctan ( 1.894 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

집단적 용어

= \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1} - \frac{2 arctan ( 1.894 )}{- 1}

\frac{36 0 ^{\circ} n}{- 1} = - 36 0^{\circ} n

\frac{36 0 ^{\circ} n}{- 1}

분수 규칙 적용:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{36 0 ^{\circ} n}{1}

규칙 적용

\frac{a}{1} = a

= - 36 0^{\circ} n

= - 36 0^{\circ} n - \frac{9 0 ^{\circ}}{- 1} - \frac{2 arctan ( 1.894 )}{- 1}

\frac{9 0 ^{\circ}}{- 1} = - 9 0^{\circ}

\frac{9 0 ^{\circ}}{- 1}

분수 규칙 적용:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{9 0 ^{\circ}}{1}

분수 규칙 적용:

\frac{a}{1} = a

\frac{9 0 ^{\circ}}{1} = 9 0^{\circ}

= - 9 0^{\circ}

\frac{2 arctan ( 1.894 )}{- 1} = - 2 arctan (1.894)

\frac{2 arctan ( 1.894 )}{- 1}

분수 규칙 적용:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{2 arctan ( 1.894 )}{1}

규칙 적용

\frac{a}{1} = a

= - 2 arctan (1.894)

= - 36 0^{\circ} n - (- 9 0^{\circ}) - (- 2 arctan (1.894))

규칙 적용

- (- a) = a

= - 36 0^{\circ} n + 9 0^{\circ} + 2 arctan (1.894)

x = - 36 0^{\circ} n + 9 0^{\circ} + 2 arctan (1.894)

x = - 36 0^{\circ} n + 9 0^{\circ} + 2 arctan (1.894)

x = - 36 0^{\circ} n + 9 0^{\circ} + 2 arctan (1.894)

x = - 36 0^{\circ} n + 9 0^{\circ} + 2 arctan (1.894)

모든 솔루션 결합

x = - 36 0^{\circ} n + 9 0^{\circ} - 2 arctan (1.894), x = - 36 0^{\circ} n + 9 0^{\circ} + 2 arctan (1.894)

해를 10진수 형식으로 표시

x = - 36 0^{\circ} n + 9 0^{\circ} - 2 \cdot 0.94242 \dots, x = - 36 0^{\circ} n + 9 0^{\circ} + 2 \cdot 0.94242 \dots

그래프

인기 있는 예

20/3 sin(10x)+5cos(10x)=0

\frac{20}{3} sin (10 x) + 5 cos (10 x) = 0

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cos (3 x + \frac{π}{4}) = - \frac{3}{2}

sin (x) - \frac{1}{4} = 0

sqrt(2)csc(θ)-2=0

2 csc (θ) - 2 = 0

sin(θ)=(sqrt(5))/4

sin (θ) = \frac{5}{4}