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인기 있는 삼각법 >

tan^2(45+x/3)=0.58

해법

tan^{2} (4 5^{\circ} + \frac{x}{3}) = 0.58

해법

x = 3 \cdot 0.65086 \dots + 54 0^{\circ} n - 13 5^{\circ}, x = - 3 \cdot 0.65086 \dots + 54 0^{\circ} n - 13 5^{\circ}

+1

라디안

x = 3 \cdot 0.65086 \dots - \frac{3 π}{4} + 3 πn, x = - 3 \cdot 0.65086 \dots - \frac{3 π}{4} + 3 πn

솔루션 단계

tan^{2} (4 5^{\circ} + \frac{x}{3}) = 0.58

대체로 해결

tan^{2} (4 5^{\circ} + \frac{x}{3}) = 0.58

하게:

tan (4 5^{\circ} + \frac{x}{3}) = u

u^{2} = 0.58

u^{2} = 0.58 : u = 0.58, u = - 0.58

u^{2} = 0.58

위해서

x^{2} = f (a)

해결책은

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

u = 0.58, u = - 0.58

뒤로 대체

u = tan (4 5^{\circ} + \frac{x}{3})

tan (4 5^{\circ} + \frac{x}{3}) = 0.58, tan (4 5^{\circ} + \frac{x}{3}) = - 0.58

tan (4 5^{\circ} + \frac{x}{3}) = 0.58, tan (4 5^{\circ} + \frac{x}{3}) = - 0.58

tan (4 5^{\circ} + \frac{x}{3}) = 0.58 : x = 3 arctan (0.58) + 54 0^{\circ} n - 13 5^{\circ}

tan (4 5^{\circ} + \frac{x}{3}) = 0.58

트리거 역속성 적용

tan (4 5^{\circ} + \frac{x}{3}) = 0.58

일반 솔루션

tan (4 5^{\circ} + \frac{x}{3}) = 0.58

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

4 5^{\circ} + \frac{x}{3} = arctan (0.58) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{3} = arctan (0.58) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{3} = arctan (0.58) + 18 0^{\circ} n

해결 :

x = 3 arctan (0.58) + 54 0^{\circ} n - 13 5^{\circ}

4 5^{\circ} + \frac{x}{3} = arctan (0.58) + 18 0^{\circ} n

4 5^{\circ}

를 오른쪽으로 이동

4 5^{\circ} + \frac{x}{3} = arctan (0.58) + 18 0^{\circ} n

빼다

4 5^{\circ}

양쪽에서

4 5^{\circ} + \frac{x}{3} - 4 5^{\circ} = arctan (0.58) + 18 0^{\circ} n - 4 5^{\circ}

단순화

\frac{x}{3} = arctan (0.58) + 18 0^{\circ} n - 4 5^{\circ}

\frac{x}{3} = arctan (0.58) + 18 0^{\circ} n - 4 5^{\circ}

양쪽을 곱한 값

3

\frac{x}{3} = arctan (0.58) + 18 0^{\circ} n - 4 5^{\circ}

양쪽을 곱한 값

3

\frac{3 x}{3} = 3 arctan (0.58) + 54 0^{\circ} n - 3 \cdot 4 5^{\circ}

단순화

\frac{3 x}{3} = 3 arctan (0.58) + 54 0^{\circ} n - 3 \cdot 4 5^{\circ}

\frac{3 x}{3}

간소화하다 :

x

\frac{3 x}{3}

숫자를 나눕니다:

\frac{3}{3} = 1

= x

3 arctan (0.58) + 54 0^{\circ} n - 3 \cdot 4 5^{\circ}

간소화하다 :

3 arctan (0.58) + 54 0^{\circ} n - 13 5^{\circ}

3 arctan (0.58) + 54 0^{\circ} n - 3 \cdot 4 5^{\circ}

3 \cdot 4 5^{\circ}

곱하다

: 13 5^{\circ}

3 \cdot 4 5^{\circ}

다중 분수:

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

= 13 5^{\circ}

= 3 arctan (0.58) + 54 0^{\circ} n - 13 5^{\circ}

x = 3 arctan (0.58) + 54 0^{\circ} n - 13 5^{\circ}

x = 3 arctan (0.58) + 54 0^{\circ} n - 13 5^{\circ}

x = 3 arctan (0.58) + 54 0^{\circ} n - 13 5^{\circ}

x = 3 arctan (0.58) + 54 0^{\circ} n - 13 5^{\circ}

tan (4 5^{\circ} + \frac{x}{3}) = - 0.58 : x = - 3 arctan (\frac{29}{5 2}) + 54 0^{\circ} n - 13 5^{\circ}

tan (4 5^{\circ} + \frac{x}{3}) = - 0.58

트리거 역속성 적용

tan (4 5^{\circ} + \frac{x}{3}) = - 0.58

일반 솔루션

tan (4 5^{\circ} + \frac{x}{3}) = - 0.58

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

4 5^{\circ} + \frac{x}{3} = arctan (- 0.58) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{3} = arctan (- 0.58) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{3} = arctan (- 0.58) + 18 0^{\circ} n

해결 :

x = - 3 arctan (\frac{29}{5 2}) + 54 0^{\circ} n - 13 5^{\circ}

4 5^{\circ} + \frac{x}{3} = arctan (- 0.58) + 18 0^{\circ} n

arctan (- 0.58) + 18 0^{\circ} n

간소화하다 :

- arctan (\frac{29}{5 2}) + 18 0^{\circ} n

arctan (- 0.58) + 18 0^{\circ} n

arctan (- 0.58) = - arctan (\frac{58}{10})

arctan (- 0.58)

= arctan (- \frac{29}{50})

다음 속성을 사용하십시오:

arctan (- x) = - arctan (x)

arctan (- \frac{29}{50}) = - arctan (\frac{29}{50})

= - arctan (\frac{29}{50})

= - arctan (\frac{58}{10})

= - arctan (\frac{58}{10}) + 18 0^{\circ} n

\frac{58}{10} = \frac{29}{5 2}

\frac{58}{10}

58

요인:

229

58 = 2 \cdot 29

인수

= 2 \cdot 29

급진적인 규칙 적용:

n ab = n a n b

= 229

10

요인:

2 \cdot 5

10 = 2 \cdot 5

인수

= \frac{2 29}{2 \cdot 5}

\frac{2 29}{2 \cdot 5}

취소하다 :

\frac{29}{2 \cdot 5}

\frac{2 29}{2 \cdot 5}

급진적인 규칙 적용:

n a = a^{\frac{1}{n}}

2 = 2^{\frac{1}{2}}

= \frac{2 ^{\frac{1}{2}} 29}{2 \cdot 5}

지수 규칙 적용:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{2 ^{\frac{1}{2}}}{2 ^{1}} = \frac{1}{2 ^{1 - \frac{1}{2}}}

= \frac{29}{5 \cdot 2 ^{- \frac{1}{2} + 1}}

숫자를 빼세요:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{29}{5 \cdot 2 ^{\frac{1}{2}}}

급진적인 규칙 적용:

a^{\frac{1}{n}} = n a

2^{\frac{1}{2}} = 2

= \frac{29}{5 2}

= \frac{29}{2 \cdot 5}

= - arctan (\frac{29}{5 2}) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{3} = - arctan (\frac{29}{5 2}) + 18 0^{\circ} n

4 5^{\circ}

를 오른쪽으로 이동

4 5^{\circ} + \frac{x}{3} = - arctan (\frac{29}{5 2}) + 18 0^{\circ} n

빼다

4 5^{\circ}

양쪽에서

4 5^{\circ} + \frac{x}{3} - 4 5^{\circ} = - arctan (\frac{29}{5 2}) + 18 0^{\circ} n - 4 5^{\circ}

단순화

4 5^{\circ} + \frac{x}{3} - 4 5^{\circ} = - arctan (\frac{29}{5 2}) + 18 0^{\circ} n - 4 5^{\circ}

4 5^{\circ} + \frac{x}{3} - 4 5^{\circ}

간소화하다 :

\frac{x}{3}

4 5^{\circ} + \frac{x}{3} - 4 5^{\circ}

유사 요소 추가:

4 5^{\circ} - 4 5^{\circ} = 0

= \frac{x}{3}

- arctan (\frac{29}{5 2}) + 18 0^{\circ} n - 4 5^{\circ}

간소화하다 :

- arctan (\frac{29}{5 2}) + 18 0^{\circ} n - 4 5^{\circ}

- arctan (\frac{29}{5 2}) + 18 0^{\circ} n - 4 5^{\circ}

= - arctan (\frac{58}{10}) + 18 0^{\circ} n - 4 5^{\circ}

\frac{58}{10} = \frac{29}{5 2}

\frac{58}{10}

58

요인:

229

58 = 2 \cdot 29

인수

= 2 \cdot 29

급진적인 규칙 적용:

n ab = n a n b

= 229

10

요인:

2 \cdot 5

10 = 2 \cdot 5

인수

= \frac{2 29}{2 \cdot 5}

\frac{2 29}{2 \cdot 5}

취소하다 :

\frac{29}{2 \cdot 5}

\frac{2 29}{2 \cdot 5}

급진적인 규칙 적용:

n a = a^{\frac{1}{n}}

2 = 2^{\frac{1}{2}}

= \frac{2 ^{\frac{1}{2}} 29}{2 \cdot 5}

지수 규칙 적용:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{2 ^{\frac{1}{2}}}{2 ^{1}} = \frac{1}{2 ^{1 - \frac{1}{2}}}

= \frac{29}{5 \cdot 2 ^{- \frac{1}{2} + 1}}

숫자를 빼세요:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{29}{5 \cdot 2 ^{\frac{1}{2}}}

급진적인 규칙 적용:

a^{\frac{1}{n}} = n a

2^{\frac{1}{2}} = 2

= \frac{29}{5 2}

= \frac{29}{2 \cdot 5}

= - arctan (\frac{29}{5 2}) + 18 0^{\circ} n - 4 5^{\circ}

더 이상 단순화할 수 없습니다

= - arctan (\frac{29}{5 2}) + 18 0^{\circ} n - 4 5^{\circ}

\frac{x}{3} = - arctan (\frac{29}{5 2}) + 18 0^{\circ} n - 4 5^{\circ}

\frac{x}{3} = - arctan (\frac{29}{5 2}) + 18 0^{\circ} n - 4 5^{\circ}

\frac{x}{3} = - arctan (\frac{29}{5 2}) + 18 0^{\circ} n - 4 5^{\circ}

양쪽을 곱한 값

3

\frac{x}{3} = - arctan (\frac{29}{5 2}) + 18 0^{\circ} n - 4 5^{\circ}

양쪽을 곱한 값

3

\frac{3 x}{3} = - 3 arctan (\frac{29}{5 2}) + 54 0^{\circ} n - 3 \cdot 4 5^{\circ}

단순화

\frac{3 x}{3} = - 3 arctan (\frac{29}{5 2}) + 54 0^{\circ} n - 3 \cdot 4 5^{\circ}

\frac{3 x}{3}

간소화하다 :

x

\frac{3 x}{3}

숫자를 나눕니다:

\frac{3}{3} = 1

= x

- 3 arctan (\frac{29}{5 2}) + 54 0^{\circ} n - 3 \cdot 4 5^{\circ}

간소화하다 :

- 3 arctan (\frac{29}{5 2}) + 54 0^{\circ} n - 13 5^{\circ}

- 3 arctan (\frac{29}{5 2}) + 54 0^{\circ} n - 3 \cdot 4 5^{\circ}

arctan (\frac{29}{5 2})

단순화하세요:

arctan (\frac{58}{10})

arctan (\frac{29}{5 2})

= arctan (\frac{58}{10})

= - 3 arctan (\frac{58}{10}) + 54 0^{\circ} n - 3 \cdot 4 5^{\circ}

3 \cdot 4 5^{\circ}

곱하다

: 13 5^{\circ}

3 \cdot 4 5^{\circ}

다중 분수:

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

= 13 5^{\circ}

= - 3 arctan (\frac{58}{10}) + 54 0^{\circ} n - 13 5^{\circ}

\frac{58}{10} = \frac{29}{5 2}

\frac{58}{10}

58

요인:

229

58 = 2 \cdot 29

인수

= 2 \cdot 29

급진적인 규칙 적용:

n ab = n a n b

= 229

10

요인:

2 \cdot 5

10 = 2 \cdot 5

인수

= \frac{2 29}{2 \cdot 5}

\frac{2 29}{2 \cdot 5}

취소하다 :

\frac{29}{2 \cdot 5}

\frac{2 29}{2 \cdot 5}

급진적인 규칙 적용:

n a = a^{\frac{1}{n}}

2 = 2^{\frac{1}{2}}

= \frac{2 ^{\frac{1}{2}} 29}{2 \cdot 5}

지수 규칙 적용:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{2 ^{\frac{1}{2}}}{2 ^{1}} = \frac{1}{2 ^{1 - \frac{1}{2}}}

= \frac{29}{5 \cdot 2 ^{- \frac{1}{2} + 1}}

숫자를 빼세요:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{29}{5 \cdot 2 ^{\frac{1}{2}}}

급진적인 규칙 적용:

a^{\frac{1}{n}} = n a

2^{\frac{1}{2}} = 2

= \frac{29}{5 2}

= \frac{29}{2 \cdot 5}

= - 3 arctan (\frac{29}{5 2}) + 54 0^{\circ} n - 13 5^{\circ}

x = - 3 arctan (\frac{29}{5 2}) + 54 0^{\circ} n - 13 5^{\circ}

x = - 3 arctan (\frac{29}{5 2}) + 54 0^{\circ} n - 13 5^{\circ}

x = - 3 arctan (\frac{29}{5 2}) + 54 0^{\circ} n - 13 5^{\circ}

x = - 3 arctan (\frac{29}{5 2}) + 54 0^{\circ} n - 13 5^{\circ}

모든 솔루션 결합

x = 3 arctan (0.58) + 54 0^{\circ} n - 13 5^{\circ}, x = - 3 arctan (\frac{29}{5 2}) + 54 0^{\circ} n - 13 5^{\circ}

해를 10진수 형식으로 표시

x = 3 \cdot 0.65086 \dots + 54 0^{\circ} n - 13 5^{\circ}, x = - 3 \cdot 0.65086 \dots + 54 0^{\circ} n - 13 5^{\circ}

그래프

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