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인기 있는 삼각법 >

3.87sin((2pi(t+101.75))/(365))+11.7=14

해법

3.87 sin (\frac{2 π ( t + 101.75 )}{365}) + 11.7 = 14

해법

t = \frac{365 \cdot 0.63641 \dots}{2 π} + 365 n - 101.75, t = \frac{365}{2} - \frac{365 \cdot 0.63641 \dots}{2 π} + 365 n - 101.75

+1

도

t = - 3711.60484 \dots^{\circ} + 20912.95952 \dots^{\circ} n, t = 2508.39347 \dots^{\circ} + 20912.95952 \dots^{\circ} n

솔루션 단계

3.87 sin (\frac{2 π ( t + 101.75 )}{365}) + 11.7 = 14

양쪽을 곱한 값

100

3.87 sin (\frac{2 π ( t + 101.75 )}{365}) + 11.7 = 14

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

3.87 sin (\frac{2 π ( t + 101.75 )}{365}) \cdot 100 + 11.7 \cdot 100 = 14 \cdot 100

다듬다

387 sin (\frac{2 π ( t + 101.75 )}{365}) + 1170 = 1400

387 sin (\frac{2 π ( t + 101.75 )}{365}) + 1170 = 1400

1170

를 오른쪽으로 이동

387 sin (\frac{2 π ( t + 101.75 )}{365}) + 1170 = 1400

빼다

1170

양쪽에서

387 sin (\frac{2 π ( t + 101.75 )}{365}) + 1170 - 1170 = 1400 - 1170

단순화

387 sin (\frac{2 π ( t + 101.75 )}{365}) = 230

387 sin (\frac{2 π ( t + 101.75 )}{365}) = 230

양쪽을 다음으로 나눕니다

387

387 sin (\frac{2 π ( t + 101.75 )}{365}) = 230

양쪽을 다음으로 나눕니다

387

\frac{387 sin ( \frac{2 π ( t + 101.75 )}{365} )}{387} = \frac{230}{387}

단순화

sin (\frac{2 π ( t + 101.75 )}{365}) = \frac{230}{387}

sin (\frac{2 π ( t + 101.75 )}{365}) = \frac{230}{387}

트리거 역속성 적용

sin (\frac{2 π ( t + 101.75 )}{365}) = \frac{230}{387}

일반 솔루션

sin (\frac{2 π ( t + 101.75 )}{365}) = \frac{230}{387}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

\frac{2 π ( t + 101.75 )}{365} = arcsin (\frac{230}{387}) + 2 πn, \frac{2 π ( t + 101.75 )}{365} = π - arcsin (\frac{230}{387}) + 2 πn

\frac{2 π ( t + 101.75 )}{365} = arcsin (\frac{230}{387}) + 2 πn, \frac{2 π ( t + 101.75 )}{365} = π - arcsin (\frac{230}{387}) + 2 πn

\frac{2 π ( t + 101.75 )}{365} = arcsin (\frac{230}{387}) + 2 πn

해결 :

t = \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n - 101.75

\frac{2 π ( t + 101.75 )}{365} = arcsin (\frac{230}{387}) + 2 πn

양쪽을 곱한 값

365

\frac{2 π ( t + 101.75 )}{365} = arcsin (\frac{230}{387}) + 2 πn

양쪽을 곱한 값

365

\frac{365 \cdot 2 π ( t + 101.75 )}{365} = 365 arcsin (\frac{230}{387}) + 365 \cdot 2 πn

단순화

\frac{365 \cdot 2 π ( t + 101.75 )}{365} = 365 arcsin (\frac{230}{387}) + 365 \cdot 2 πn

\frac{365 \cdot 2 π ( t + 101.75 )}{365}

간소화하다 :

2 π (t + 101.75)

\frac{365 \cdot 2 π ( t + 101.75 )}{365}

숫자를 곱하시오:

365 \cdot 2 = 730

= \frac{730 π ( t + 101.75 )}{365}

숫자를 나눕니다:

\frac{730}{365} = 2

= 2 π (t + 101.75)

365 arcsin (\frac{230}{387}) + 365 \cdot 2 πn

간소화하다 :

365 arcsin (\frac{230}{387}) + 730 πn

365 arcsin (\frac{230}{387}) + 365 \cdot 2 πn

숫자를 곱하시오:

365 \cdot 2 = 730

= 365 arcsin (\frac{230}{387}) + 730 πn

2 π (t + 101.75) = 365 arcsin (\frac{230}{387}) + 730 πn

2 π (t + 101.75) = 365 arcsin (\frac{230}{387}) + 730 πn

2 π (t + 101.75) = 365 arcsin (\frac{230}{387}) + 730 πn

양쪽을 다음으로 나눕니다

2 π

2 π (t + 101.75) = 365 arcsin (\frac{230}{387}) + 730 πn

양쪽을 다음으로 나눕니다

2 π

\frac{2 π ( t + 101.75 )}{2 π} = \frac{365 arcsin ( \frac{230}{387} )}{2 π} + \frac{730 πn}{2 π}

단순화

\frac{2 π ( t + 101.75 )}{2 π} = \frac{365 arcsin ( \frac{230}{387} )}{2 π} + \frac{730 πn}{2 π}

\frac{2 π ( t + 101.75 )}{2 π}

간소화하다 :

t + 101.75

\frac{2 π ( t + 101.75 )}{2 π}

숫자를 나눕니다:

\frac{2}{2} = 1

= \frac{π ( t + 101.75 )}{π}

공통 요인 취소:

π

= t + 101.75

\frac{365 arcsin ( \frac{230}{387} )}{2 π} + \frac{730 πn}{2 π}

간소화하다 :

\frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n

\frac{365 arcsin ( \frac{230}{387} )}{2 π} + \frac{730 πn}{2 π}

\frac{730 πn}{2 π}

취소하다 :

365 n

\frac{730 πn}{2 π}

\frac{730 πn}{2 π}

취소하다 :

365 n

\frac{730 πn}{2 π}

숫자를 나눕니다:

\frac{730}{2} = 365

= \frac{365 πn}{π}

공통 요인 취소:

π

= 365 n

= 365 n

= \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n

t + 101.75 = \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n

t + 101.75 = \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n

t + 101.75 = \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n

101.75

를 오른쪽으로 이동

t + 101.75 = \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n

빼다

101.75

양쪽에서

t + 101.75 - 101.75 = \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n - 101.75

단순화

t = \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n - 101.75

t = \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n - 101.75

\frac{2 π ( t + 101.75 )}{365} = π - arcsin (\frac{230}{387}) + 2 πn

해결 :

t = \frac{365}{2} - \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n - 101.75

\frac{2 π ( t + 101.75 )}{365} = π - arcsin (\frac{230}{387}) + 2 πn

양쪽을 곱한 값

365

\frac{2 π ( t + 101.75 )}{365} = π - arcsin (\frac{230}{387}) + 2 πn

양쪽을 곱한 값

365

\frac{365 \cdot 2 π ( t + 101.75 )}{365} = 365 π - 365 arcsin (\frac{230}{387}) + 365 \cdot 2 πn

단순화

\frac{365 \cdot 2 π ( t + 101.75 )}{365} = 365 π - 365 arcsin (\frac{230}{387}) + 365 \cdot 2 πn

\frac{365 \cdot 2 π ( t + 101.75 )}{365}

간소화하다 :

2 π (t + 101.75)

\frac{365 \cdot 2 π ( t + 101.75 )}{365}

숫자를 곱하시오:

365 \cdot 2 = 730

= \frac{730 π ( t + 101.75 )}{365}

숫자를 나눕니다:

\frac{730}{365} = 2

= 2 π (t + 101.75)

365 π - 365 arcsin (\frac{230}{387}) + 365 \cdot 2 πn

간소화하다 :

365 π - 365 arcsin (\frac{230}{387}) + 730 πn

365 π - 365 arcsin (\frac{230}{387}) + 365 \cdot 2 πn

숫자를 곱하시오:

365 \cdot 2 = 730

= 365 π - 365 arcsin (\frac{230}{387}) + 730 πn

2 π (t + 101.75) = 365 π - 365 arcsin (\frac{230}{387}) + 730 πn

2 π (t + 101.75) = 365 π - 365 arcsin (\frac{230}{387}) + 730 πn

2 π (t + 101.75) = 365 π - 365 arcsin (\frac{230}{387}) + 730 πn

양쪽을 다음으로 나눕니다

2 π

2 π (t + 101.75) = 365 π - 365 arcsin (\frac{230}{387}) + 730 πn

양쪽을 다음으로 나눕니다

2 π

\frac{2 π ( t + 101.75 )}{2 π} = \frac{365 π}{2 π} - \frac{365 arcsin ( \frac{230}{387} )}{2 π} + \frac{730 πn}{2 π}

단순화

\frac{2 π ( t + 101.75 )}{2 π} = \frac{365 π}{2 π} - \frac{365 arcsin ( \frac{230}{387} )}{2 π} + \frac{730 πn}{2 π}

\frac{2 π ( t + 101.75 )}{2 π}

간소화하다 :

t + 101.75

\frac{2 π ( t + 101.75 )}{2 π}

숫자를 나눕니다:

\frac{2}{2} = 1

= \frac{π ( t + 101.75 )}{π}

공통 요인 취소:

π

= t + 101.75

\frac{365 π}{2 π} - \frac{365 arcsin ( \frac{230}{387} )}{2 π} + \frac{730 πn}{2 π}

간소화하다 :

\frac{365}{2} - \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n

\frac{365 π}{2 π} - \frac{365 arcsin ( \frac{230}{387} )}{2 π} + \frac{730 πn}{2 π}

\frac{365 π}{2 π}

취소하다 :

\frac{365}{2}

\frac{365 π}{2 π}

공통 요인 취소:

π

= \frac{365}{2}

= \frac{365}{2} - \frac{365 arcsin ( \frac{230}{387} )}{2 π} + \frac{730 πn}{2 π}

\frac{730 πn}{2 π}

취소하다 :

365 n

\frac{730 πn}{2 π}

\frac{730 πn}{2 π}

취소하다 :

365 n

\frac{730 πn}{2 π}

숫자를 나눕니다:

\frac{730}{2} = 365

= \frac{365 πn}{π}

공통 요인 취소:

π

= 365 n

= 365 n

= \frac{365}{2} - \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n

t + 101.75 = \frac{365}{2} - \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n

t + 101.75 = \frac{365}{2} - \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n

t + 101.75 = \frac{365}{2} - \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n

101.75

를 오른쪽으로 이동

t + 101.75 = \frac{365}{2} - \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n

빼다

101.75

양쪽에서

t + 101.75 - 101.75 = \frac{365}{2} - \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n - 101.75

단순화

t = \frac{365}{2} - \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n - 101.75

t = \frac{365}{2} - \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n - 101.75

t = \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n - 101.75, t = \frac{365}{2} - \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n - 101.75

해를 10진수 형식으로 표시

t = \frac{365 \cdot 0.63641 \dots}{2 π} + 365 n - 101.75, t = \frac{365}{2} - \frac{365 \cdot 0.63641 \dots}{2 π} + 365 n - 101.75

그래프

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