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인기 있는 삼각법 >

250sin(75)=393.19sin(45-θ)

해법

250 sin (7 5^{\circ}) = 393.19 sin (4 5^{\circ} - θ)

해법

θ = - 36 0^{\circ} n + 4 5^{\circ} - 0.66132 \dots, θ = - 18 0^{\circ} - 36 0^{\circ} n + 4 5^{\circ} + 0.66132 \dots

+1

라디안

θ = \frac{π}{4} - 0.66132 \dots - 2 πn, θ = - π + \frac{π}{4} + 0.66132 \dots - 2 πn

솔루션 단계

250 sin (7 5^{\circ}) = 393.19 sin (4 5^{\circ} - θ)

sin (7 5^{\circ}) = \frac{6 + 2}{4}

sin (7 5^{\circ})

삼각성을 사용하여 다시 쓰기:

sin (4 5^{\circ}) cos (3 0^{\circ}) + cos (4 5^{\circ}) sin (3 0^{\circ})

sin (7 5^{\circ})

쓰다

sin (7 5^{\circ})

로

sin (4 5^{\circ} + 3 0^{\circ})

= sin (4 5^{\circ} + 3 0^{\circ})

앵글섬식별사용:

sin (s + t) = sin (s) cos (t) + cos (s) sin (t)

= sin (4 5^{\circ}) cos (3 0^{\circ}) + cos (4 5^{\circ}) sin (3 0^{\circ})

= sin (4 5^{\circ}) cos (3 0^{\circ}) + cos (4 5^{\circ}) sin (3 0^{\circ})

다음과 같은 사소한 아이덴티티 사용:

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\circ})

sin (x)

주기율표

36 0^{\circ} n

주기:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

다음과 같은 사소한 아이덴티티 사용:

cos (3 0^{\circ}) = \frac{3}{2}

cos (3 0^{\circ})

cos (x)

주기율표

36 0^{\circ} n

주기:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{3}{2}

다음과 같은 사소한 아이덴티티 사용:

cos (4 5^{\circ}) = \frac{2}{2}

cos (4 5^{\circ})

cos (x)

주기율표

36 0^{\circ} n

주기:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{2}{2}

다음과 같은 사소한 아이덴티티 사용:

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 0^{\circ})

sin (x)

주기율표

36 0^{\circ} n

주기:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

= \frac{2}{2} \cdot \frac{3}{2} + \frac{2}{2} \cdot \frac{1}{2}

\frac{2}{2} \cdot \frac{3}{2} + \frac{2}{2} \cdot \frac{1}{2}

간소화하다 :

\frac{6 + 2}{4}

\frac{2}{2} \cdot \frac{3}{2} + \frac{2}{2} \cdot \frac{1}{2}

\frac{2}{2} \cdot \frac{3}{2} = \frac{6}{4}

\frac{2}{2} \cdot \frac{3}{2}

다중 분수:

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

= \frac{2 3}{2 \cdot 2}

숫자를 곱하시오:

2 \cdot 2 = 4

= \frac{2 3}{4}

23

단순화하세요:

6

23

급진적인 규칙 적용:

a b = a \cdot b

23 = 2 \cdot 3

= 2 \cdot 3

숫자를 곱하시오:

2 \cdot 3 = 6

= 6

= \frac{6}{4}

\frac{2}{2} \cdot \frac{1}{2} = \frac{2}{4}

\frac{2}{2} \cdot \frac{1}{2}

다중 분수:

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

= \frac{2 \cdot 1}{2 \cdot 2}

곱하다:

2 \cdot 1 = 2

= \frac{2}{2 \cdot 2}

숫자를 곱하시오:

2 \cdot 2 = 4

= \frac{2}{4}

= \frac{6}{4} + \frac{2}{4}

규칙 적용

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

= \frac{6 + 2}{4}

= \frac{6 + 2}{4}

250 \cdot \frac{6 + 2}{4} = 393.19 sin (4 5^{\circ} - θ)

측면 전환

393.19 sin (4 5^{\circ} - θ) = 250 \cdot \frac{6 + 2}{4}

양쪽을 곱한 값

100

393.19 sin (4 5^{\circ} - θ) = 250 \cdot \frac{6 + 2}{4}

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

393.19 sin (4 5^{\circ} - θ) \cdot 100 = 250 \cdot \frac{6 + 2}{4} \cdot 100

다듬다

39319 sin (4 5^{\circ} - θ) = 6250 (6 + 2)

39319 sin (4 5^{\circ} - θ) = 6250 (6 + 2)

양쪽을 다음으로 나눕니다

39319

39319 sin (4 5^{\circ} - θ) = 6250 (6 + 2)

양쪽을 다음으로 나눕니다

39319

\frac{39319 sin ( 4 5 ^{\circ} - θ )}{39319} = \frac{6250 ( 6 + 2 )}{39319}

단순화

sin (4 5^{\circ} - θ) = \frac{6250 ( 6 + 2 )}{39319}

sin (4 5^{\circ} - θ) = \frac{6250 ( 6 + 2 )}{39319}

트리거 역속성 적용

sin (4 5^{\circ} - θ) = \frac{6250 ( 6 + 2 )}{39319}

일반 솔루션

sin (4 5^{\circ} - θ) = \frac{6250 ( 6 + 2 )}{39319}

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

4 5^{\circ} - θ = arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n, 4 5^{\circ} - θ = 18 0^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n

4 5^{\circ} - θ = arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n, 4 5^{\circ} - θ = 18 0^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n

4 5^{\circ} - θ = arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n

해결 :

θ = - 36 0^{\circ} n + 4 5^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319})

4 5^{\circ} - θ = arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n

4 5^{\circ}

를 오른쪽으로 이동

4 5^{\circ} - θ = arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n

빼다

4 5^{\circ}

양쪽에서

4 5^{\circ} - θ - 4 5^{\circ} = arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n - 4 5^{\circ}

단순화

- θ = arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n - 4 5^{\circ}

- θ = arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n - 4 5^{\circ}

양쪽을 다음으로 나눕니다

- 1

- θ = arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n - 4 5^{\circ}

양쪽을 다음으로 나눕니다

- 1

\frac{- θ}{- 1} = \frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{4 5 ^{\circ}}{- 1}

단순화

\frac{- θ}{- 1} = \frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{4 5 ^{\circ}}{- 1}

\frac{- θ}{- 1}

간소화하다 :

θ

\frac{- θ}{- 1}

분수 규칙 적용:

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

= \frac{θ}{1}

규칙 적용

\frac{a}{1} = a

= θ

\frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{4 5 ^{\circ}}{- 1}

간소화하다 :

- 36 0^{\circ} n + 4 5^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319})

\frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{4 5 ^{\circ}}{- 1}

집단적 용어

= \frac{36 0 ^{\circ} n}{- 1} - \frac{4 5 ^{\circ}}{- 1} + \frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 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{4 5 ^{\circ}}{- 1} + \frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1}

\frac{4 5 ^{\circ}}{- 1} = - 4 5^{\circ}

\frac{4 5 ^{\circ}}{- 1}

분수 규칙 적용:

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

= - \frac{4 5 ^{\circ}}{1}

분수 규칙 적용:

\frac{a}{1} = a

\frac{4 5 ^{\circ}}{1} = 4 5^{\circ}

= - 4 5^{\circ}

\frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1} = - arcsin (\frac{6250 ( 6 + 2 )}{39319})

\frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1}

분수 규칙 적용:

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

= - \frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{1}

분수 규칙 적용:

\frac{a}{1} = a

\frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{1} = arcsin (\frac{6250 ( 6 + 2 )}{39319})

= - arcsin (\frac{6250 ( 6 + 2 )}{39319})

= - 36 0^{\circ} n - (- 4 5^{\circ}) - arcsin (\frac{6250 ( 6 + 2 )}{39319})

규칙 적용

- (- a) = a

= - 36 0^{\circ} n + 4 5^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319})

θ = - 36 0^{\circ} n + 4 5^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319})

θ = - 36 0^{\circ} n + 4 5^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319})

θ = - 36 0^{\circ} n + 4 5^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319})

4 5^{\circ} - θ = 18 0^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n

해결 :

θ = - 18 0^{\circ} - 36 0^{\circ} n + 4 5^{\circ} + arcsin (\frac{6250 ( 6 + 2 )}{39319})

4 5^{\circ} - θ = 18 0^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n

4 5^{\circ}

를 오른쪽으로 이동

4 5^{\circ} - θ = 18 0^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n

빼다

4 5^{\circ}

양쪽에서

4 5^{\circ} - θ - 4 5^{\circ} = 18 0^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n - 4 5^{\circ}

단순화

- θ = 18 0^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n - 4 5^{\circ}

- θ = 18 0^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n - 4 5^{\circ}

양쪽을 다음으로 나눕니다

- 1

- θ = 18 0^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n - 4 5^{\circ}

양쪽을 다음으로 나눕니다

- 1

\frac{- θ}{- 1} = \frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{4 5 ^{\circ}}{- 1}

단순화

\frac{- θ}{- 1} = \frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{4 5 ^{\circ}}{- 1}

\frac{- θ}{- 1}

간소화하다 :

θ

\frac{- θ}{- 1}

분수 규칙 적용:

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

= \frac{θ}{1}

규칙 적용

\frac{a}{1} = a

= θ

\frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{4 5 ^{\circ}}{- 1}

간소화하다 :

- 18 0^{\circ} - 36 0^{\circ} n + 4 5^{\circ} + arcsin (\frac{6250 ( 6 + 2 )}{39319})

\frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{4 5 ^{\circ}}{- 1}

집단적 용어

= \frac{18 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{4 5 ^{\circ}}{- 1} - \frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1}

\frac{18 0 ^{\circ}}{- 1} = - 18 0^{\circ}

\frac{18 0 ^{\circ}}{- 1}

분수 규칙 적용:

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

= - 18 0^{\circ}

규칙 적용

\frac{a}{1} = a

= - 18 0^{\circ}

= - 18 0^{\circ} + \frac{36 0 ^{\circ} n}{- 1} - \frac{4 5 ^{\circ}}{- 1} - \frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 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

= - 18 0^{\circ} - 36 0^{\circ} n - \frac{4 5 ^{\circ}}{- 1} - \frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1}

\frac{4 5 ^{\circ}}{- 1} = - 4 5^{\circ}

\frac{4 5 ^{\circ}}{- 1}

분수 규칙 적용:

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

= - \frac{4 5 ^{\circ}}{1}

분수 규칙 적용:

\frac{a}{1} = a

\frac{4 5 ^{\circ}}{1} = 4 5^{\circ}

= - 4 5^{\circ}

\frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1} = - arcsin (\frac{6250 ( 6 + 2 )}{39319})

\frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1}

분수 규칙 적용:

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

= - \frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{1}

분수 규칙 적용:

\frac{a}{1} = a

\frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{1} = arcsin (\frac{6250 ( 6 + 2 )}{39319})

= - arcsin (\frac{6250 ( 6 + 2 )}{39319})

= - 18 0^{\circ} - 36 0^{\circ} n - (- 4 5^{\circ}) - (- arcsin (\frac{6250 ( 6 + 2 )}{39319}))

규칙 적용

- (- a) = a

= - 18 0^{\circ} - 36 0^{\circ} n + 4 5^{\circ} + arcsin (\frac{6250 ( 6 + 2 )}{39319})

θ = - 18 0^{\circ} - 36 0^{\circ} n + 4 5^{\circ} + arcsin (\frac{6250 ( 6 + 2 )}{39319})

θ = - 18 0^{\circ} - 36 0^{\circ} n + 4 5^{\circ} + arcsin (\frac{6250 ( 6 + 2 )}{39319})

θ = - 18 0^{\circ} - 36 0^{\circ} n + 4 5^{\circ} + arcsin (\frac{6250 ( 6 + 2 )}{39319})

θ = - 36 0^{\circ} n + 4 5^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319}), θ = - 18 0^{\circ} - 36 0^{\circ} n + 4 5^{\circ} + arcsin (\frac{6250 ( 6 + 2 )}{39319})

해를 10진수 형식으로 표시

θ = - 36 0^{\circ} n + 4 5^{\circ} - 0.66132 \dots, θ = - 18 0^{\circ} - 36 0^{\circ} n + 4 5^{\circ} + 0.66132 \dots

그래프

인기 있는 예

tan(θ)= 6/(6.71)

tan (θ) = \frac{6}{6.71}

sin (2 θ) = 0.5

cos (\frac{π}{2} + x) = 0

4sin(x)-13=2cos^2(x)-9

4 sin (x) - 13 = 2 cos^{2} (x) - 9

cos (θ) = - \frac{8}{11}