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인기 있는 삼각법 >

sin(2t-pi/5)=-1/3

해법

sin (2 t - \frac{π}{5}) = - \frac{1}{3}

해법

t = πn + \frac{π}{10} - \frac{0.33983 \dots}{2}, t = πn + \frac{π}{2} + \frac{π}{10} + \frac{0.33983 \dots}{2}

+1

도

t = 8.26438 \dots^{\circ} + 18 0^{\circ} n, t = 117.73561 \dots^{\circ} + 18 0^{\circ} n

솔루션 단계

sin (2 t - \frac{π}{5}) = - \frac{1}{3}

트리거 역속성 적용

sin (2 t - \frac{π}{5}) = - \frac{1}{3}

일반 솔루션

sin (2 t - \frac{π}{5}) = - \frac{1}{3}

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

2 t - \frac{π}{5} = arcsin (- \frac{1}{3}) + 2 πn, 2 t - \frac{π}{5} = π + arcsin (\frac{1}{3}) + 2 πn

2 t - \frac{π}{5} = arcsin (- \frac{1}{3}) + 2 πn, 2 t - \frac{π}{5} = π + arcsin (\frac{1}{3}) + 2 πn

2 t - \frac{π}{5} = arcsin (- \frac{1}{3}) + 2 πn

해결 :

t = πn + \frac{π}{10} - \frac{arcsin ( \frac{1}{3} )}{2}

2 t - \frac{π}{5} = arcsin (- \frac{1}{3}) + 2 πn

arcsin (- \frac{1}{3}) + 2 πn

간소화하다 :

- arcsin (\frac{1}{3}) + 2 πn

arcsin (- \frac{1}{3}) + 2 πn

다음 속성을 사용하십시오:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{1}{3}) = - arcsin (\frac{1}{3})

= - arcsin (\frac{1}{3}) + 2 πn

2 t - \frac{π}{5} = - arcsin (\frac{1}{3}) + 2 πn

\frac{π}{5}

를 오른쪽으로 이동

2 t - \frac{π}{5} = - arcsin (\frac{1}{3}) + 2 πn

더하다

\frac{π}{5}

양쪽으로

2 t - \frac{π}{5} + \frac{π}{5} = - arcsin (\frac{1}{3}) + 2 πn + \frac{π}{5}

단순화

2 t = - arcsin (\frac{1}{3}) + 2 πn + \frac{π}{5}

2 t = - arcsin (\frac{1}{3}) + 2 πn + \frac{π}{5}

양쪽을 다음으로 나눕니다

2

2 t = - arcsin (\frac{1}{3}) + 2 πn + \frac{π}{5}

양쪽을 다음으로 나눕니다

2

\frac{2 t}{2} = - \frac{arcsin ( \frac{1}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{5}}{2}

단순화

\frac{2 t}{2} = - \frac{arcsin ( \frac{1}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{5}}{2}

\frac{2 t}{2}

간소화하다 :

t

\frac{2 t}{2}

숫자를 나눕니다:

\frac{2}{2} = 1

= t

- \frac{arcsin ( \frac{1}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{5}}{2}

간소화하다 :

πn + \frac{π}{10} - \frac{arcsin ( \frac{1}{3} )}{2}

- \frac{arcsin ( \frac{1}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{5}}{2}

집단적 용어

= \frac{2 πn}{2} + \frac{\frac{π}{5}}{2} - \frac{arcsin ( \frac{1}{3} )}{2}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

숫자를 나눕니다:

\frac{2}{2} = 1

= πn

\frac{\frac{π}{5}}{2} = \frac{π}{10}

\frac{\frac{π}{5}}{2}

분수 규칙 적용:

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

= \frac{π}{5 \cdot 2}

숫자를 곱하시오:

5 \cdot 2 = 10

= \frac{π}{10}

= πn + \frac{π}{10} - \frac{arcsin ( \frac{1}{3} )}{2}

t = πn + \frac{π}{10} - \frac{arcsin ( \frac{1}{3} )}{2}

t = πn + \frac{π}{10} - \frac{arcsin ( \frac{1}{3} )}{2}

t = πn + \frac{π}{10} - \frac{arcsin ( \frac{1}{3} )}{2}

2 t - \frac{π}{5} = π + arcsin (\frac{1}{3}) + 2 πn

해결 :

t = πn + \frac{π}{2} + \frac{π}{10} + \frac{arcsin ( \frac{1}{3} )}{2}

2 t - \frac{π}{5} = π + arcsin (\frac{1}{3}) + 2 πn

\frac{π}{5}

를 오른쪽으로 이동

2 t - \frac{π}{5} = π + arcsin (\frac{1}{3}) + 2 πn

더하다

\frac{π}{5}

양쪽으로

2 t - \frac{π}{5} + \frac{π}{5} = π + arcsin (\frac{1}{3}) + 2 πn + \frac{π}{5}

단순화

2 t = π + arcsin (\frac{1}{3}) + 2 πn + \frac{π}{5}

2 t = π + arcsin (\frac{1}{3}) + 2 πn + \frac{π}{5}

양쪽을 다음으로 나눕니다

2

2 t = π + arcsin (\frac{1}{3}) + 2 πn + \frac{π}{5}

양쪽을 다음으로 나눕니다

2

\frac{2 t}{2} = \frac{π}{2} + \frac{arcsin ( \frac{1}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{5}}{2}

단순화

\frac{2 t}{2} = \frac{π}{2} + \frac{arcsin ( \frac{1}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{5}}{2}

\frac{2 t}{2}

간소화하다 :

t

\frac{2 t}{2}

숫자를 나눕니다:

\frac{2}{2} = 1

= t

\frac{π}{2} + \frac{arcsin ( \frac{1}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{5}}{2}

간소화하다 :

πn + \frac{π}{2} + \frac{π}{10} + \frac{arcsin ( \frac{1}{3} )}{2}

\frac{π}{2} + \frac{arcsin ( \frac{1}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{5}}{2}

집단적 용어

= \frac{π}{2} + \frac{2 πn}{2} + \frac{\frac{π}{5}}{2} + \frac{arcsin ( \frac{1}{3} )}{2}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

숫자를 나눕니다:

\frac{2}{2} = 1

= πn

\frac{\frac{π}{5}}{2} = \frac{π}{10}

\frac{\frac{π}{5}}{2}

분수 규칙 적용:

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

= \frac{π}{5 \cdot 2}

숫자를 곱하시오:

5 \cdot 2 = 10

= \frac{π}{10}

= \frac{π}{2} + πn + \frac{π}{10} + \frac{arcsin ( \frac{1}{3} )}{2}

집단적 용어

= πn + \frac{π}{2} + \frac{π}{10} + \frac{arcsin ( \frac{1}{3} )}{2}

t = πn + \frac{π}{2} + \frac{π}{10} + \frac{arcsin ( \frac{1}{3} )}{2}

t = πn + \frac{π}{2} + \frac{π}{10} + \frac{arcsin ( \frac{1}{3} )}{2}

t = πn + \frac{π}{2} + \frac{π}{10} + \frac{arcsin ( \frac{1}{3} )}{2}

t = πn + \frac{π}{10} - \frac{arcsin ( \frac{1}{3} )}{2}, t = πn + \frac{π}{2} + \frac{π}{10} + \frac{arcsin ( \frac{1}{3} )}{2}

해를 10진수 형식으로 표시

t = πn + \frac{π}{10} - \frac{0.33983 \dots}{2}, t = πn + \frac{π}{2} + \frac{π}{10} + \frac{0.33983 \dots}{2}

그래프

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