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인기 있는 삼각법 >

129.8sin(a)-0.6129.8cos(a)=121.79

해법

12 \cdot 9.8 \cdot sin (a) - 0.6 \cdot 12 \cdot 9.8 \cdot cos (a) = 12 \cdot 1.79

해법

a = - 2.75844 \dots + 2 πn, a = 0.69769 \dots + 2 πn

+1

도

a = - 158.04722 \dots^{\circ} + 36 0^{\circ} n, a = 39.97473 \dots^{\circ} + 36 0^{\circ} n

솔루션 단계

12 \cdot 9.8 sin (a) - 0.6 \cdot 12 \cdot 9.8 cos (a) = 12 \cdot 1.79

더하다

0.6129.8 cos (a)

양쪽으로

117.6 sin (a) = 21.48 + 70.56 cos (a)

양쪽을 제곱

(117.6 sin (a))^{2} = (21.48 + 70.56 cos (a))^{2}

빼다

(21.48 + 70.56 cos (a))^{2}

양쪽에서

13829.76 sin^{2} (a) - 461.3904 - 3031.2576 cos (a) - 4978.7136 cos^{2} (a) = 0

삼각성을 사용하여 다시 쓰기

- 461.3904 + 13829.76 sin^{2} (a) - 3031.2576 cos (a) - 4978.7136 cos^{2} (a)

피타고라스 정체성 사용:

cos^{2} (x) + sin^{2} (x) = 1

sin^{2} (x) = 1 - cos^{2} (x)

= - 461.3904 + 13829.76 (1 - cos^{2} (a)) - 3031.2576 cos (a) - 4978.7136 cos^{2} (a)

- 461.3904 + 13829.76 (1 - cos^{2} (a)) - 3031.2576 cos (a) - 4978.7136 cos^{2} (a)

간소화하다 :

- 18808.4736 cos^{2} (a) - 3031.2576 cos (a) + 13368.3696

- 461.3904 + 13829.76 (1 - cos^{2} (a)) - 3031.2576 cos (a) - 4978.7136 cos^{2} (a)

13829.76 (1 - cos^{2} (a))

확대한다:

13829.76 - 13829.76 cos^{2} (a)

13829.76 (1 - cos^{2} (a))

분배 법칙 적용:

a (b - c) = ab - a c

a = 13829.76, b = 1, c = cos^{2} (a)

= 13829.76 \cdot 1 - 13829.76 cos^{2} (a)

= 1 \cdot 13829.76 - 13829.76 cos^{2} (a)

숫자를 곱하시오:

1 \cdot 13829.76 = 13829.76

= 13829.76 - 13829.76 cos^{2} (a)

= - 461.3904 + 13829.76 - 13829.76 cos^{2} (a) - 3031.2576 cos (a) - 4978.7136 cos^{2} (a)

- 461.3904 + 13829.76 - 13829.76 cos^{2} (a) - 3031.2576 cos (a) - 4978.7136 cos^{2} (a)

단순화하세요:

- 18808.4736 cos^{2} (a) - 3031.2576 cos (a) + 13368.3696

- 461.3904 + 13829.76 - 13829.76 cos^{2} (a) - 3031.2576 cos (a) - 4978.7136 cos^{2} (a)

집단적 용어

= - 13829.76 cos^{2} (a) - 3031.2576 cos (a) - 4978.7136 cos^{2} (a) - 461.3904 + 13829.76

유사 요소 추가:

- 13829.76 cos^{2} (a) - 4978.7136 cos^{2} (a) = - 18808.4736 cos^{2} (a)

= - 18808.4736 cos^{2} (a) - 3031.2576 cos (a) - 461.3904 + 13829.76

숫자 더하기/ 빼기:

- 461.3904 + 13829.76 = 13368.3696

= - 18808.4736 cos^{2} (a) - 3031.2576 cos (a) + 13368.3696

= - 18808.4736 cos^{2} (a) - 3031.2576 cos (a) + 13368.3696

= - 18808.4736 cos^{2} (a) - 3031.2576 cos (a) + 13368.3696

13368.3696 - 18808.4736 cos^{2} (a) - 3031.2576 cos (a) = 0

대체로 해결

13368.3696 - 18808.4736 cos^{2} (a) - 3031.2576 cos (a) = 0

하게:

cos (a) = u

13368.3696 - 18808.4736 u^{2} - 3031.2576 u = 0

13368.3696 - 18808.4736 u^{2} - 3031.2576 u = 0 : u = - \frac{3031.2576 + 1014943029.424128}{37616.9472}, u = \frac{1014943029.424128 - 3031.2576}{37616.9472}

13368.3696 - 18808.4736 u^{2} - 3031.2576 u = 0

표준 양식으로 작성

a x^{2} + b x + c = 0

- 18808.4736 u^{2} - 3031.2576 u + 13368.3696 = 0

쿼드 공식으로 해결

- 18808.4736 u^{2} - 3031.2576 u + 13368.3696 = 0

4차 방정식 공식:

위해서

a = - 18808.4736, b = - 3031.2576, c = 13368.3696

u_{1, 2} = \frac{- ( - 3031.2576 ) \pm ( - 3031.2576 ) ^{2} - 4 ( - 18808.4736 ) \cdot 13368.3696}{2 ( - 18808.4736 )}

u_{1, 2} = \frac{- ( - 3031.2576 ) \pm ( - 3031.2576 ) ^{2} - 4 ( - 18808.4736 ) \cdot 13368.3696}{2 ( - 18808.4736 )}

(- 3031.2576)^{2} - 4 (- 18808.4736) \cdot 13368.3696 = 1014943029.424128

(- 3031.2576)^{2} - 4 (- 18808.4736) \cdot 13368.3696

규칙 적용

- (- a) = a

= (- 3031.2576)^{2} + 4 \cdot 18808.4736 \cdot 13368.3696

지수 규칙 적용:

(- a)^{n} = a^{n},

이면

n

균등하다

(- 3031.2576)^{2} = 3031.257 6^{2}

= 3031.257 6^{2} + 4 \cdot 13368.3696 \cdot 18808.4736

숫자를 곱하시오:

4 \cdot 18808.4736 \cdot 13368.3696 = 1005754506.78657 \dots

= 3031.257 6^{2} + 1005754506.78657 \dots

3031.257 6^{2} = 9188522.63755 \dots

= 9188522.63755 \dots + 1005754506.78657 \dots

숫자 추가:

9188522.63755 \dots + 1005754506.78657 \dots = 1014943029.424128

= 1014943029.424128

u_{1, 2} = \frac{- ( - 3031.2576 ) \pm 1014943029.424128}{2 ( - 18808.4736 )}

솔루션 분리

u_{1} = \frac{- ( - 3031.2576 ) + 1014943029.424128}{2 ( - 18808.4736 )}, u_{2} = \frac{- ( - 3031.2576 ) - 1014943029.424128}{2 ( - 18808.4736 )}

u = \frac{- ( - 3031.2576 ) + 1014943029.424128}{2 ( - 18808.4736 )} : - \frac{3031.2576 + 1014943029.424128}{37616.9472}

\frac{- ( - 3031.2576 ) + 1014943029.424128}{2 ( - 18808.4736 )}

괄호 제거:

(- a) = - a, - (- a) = a

= \frac{3031.2576 + 1014943029.424128}{- 2 \cdot 18808.4736}

숫자를 곱하시오:

2 \cdot 18808.4736 = 37616.9472

= \frac{3031.2576 + 1014943029.424128}{- 37616.9472}

분수 규칙 적용:

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

= - \frac{3031.2576 + 1014943029.424128}{37616.9472}

u = \frac{- ( - 3031.2576 ) - 1014943029.424128}{2 ( - 18808.4736 )} : \frac{1014943029.424128 - 3031.2576}{37616.9472}

\frac{- ( - 3031.2576 ) - 1014943029.424128}{2 ( - 18808.4736 )}

괄호 제거:

(- a) = - a, - (- a) = a

= \frac{3031.2576 - 1014943029.424128}{- 2 \cdot 18808.4736}

숫자를 곱하시오:

2 \cdot 18808.4736 = 37616.9472

= \frac{3031.2576 - 1014943029.424128}{- 37616.9472}

분수 규칙 적용:

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

3031.2576 - 1014943029.424128 = - (1014943029.424128 - 3031.2576)

= \frac{1014943029.424128 - 3031.2576}{37616.9472}

2차 방정식의 해는 다음과 같다:

u = - \frac{3031.2576 + 1014943029.424128}{37616.9472}, u = \frac{1014943029.424128 - 3031.2576}{37616.9472}

뒤로 대체

u = cos (a)

cos (a) = - \frac{3031.2576 + 1014943029.424128}{37616.9472}, cos (a) = \frac{1014943029.424128 - 3031.2576}{37616.9472}

cos (a) = - \frac{3031.2576 + 1014943029.424128}{37616.9472}, cos (a) = \frac{1014943029.424128 - 3031.2576}{37616.9472}

cos (a) = - \frac{3031.2576 + 1014943029.424128}{37616.9472} : a = arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn, a = - arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn

cos (a) = - \frac{3031.2576 + 1014943029.424128}{37616.9472}

트리거 역속성 적용

cos (a) = - \frac{3031.2576 + 1014943029.424128}{37616.9472}

일반 솔루션

cos (a) = - \frac{3031.2576 + 1014943029.424128}{37616.9472}

cos (x) = - a \Rightarrow x = arccos (- a) + 2 πn, x = - arccos (- a) + 2 πn

a = arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn, a = - arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn

a = arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn, a = - arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn

cos (a) = \frac{1014943029.424128 - 3031.2576}{37616.9472} : a = arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn, a = 2 π - arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn

cos (a) = \frac{1014943029.424128 - 3031.2576}{37616.9472}

트리거 역속성 적용

cos (a) = \frac{1014943029.424128 - 3031.2576}{37616.9472}

일반 솔루션

cos (a) = \frac{1014943029.424128 - 3031.2576}{37616.9472}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

a = arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn, a = 2 π - arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn

a = arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn, a = 2 π - arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn

모든 솔루션 결합

a = arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn, a = - arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn, a = arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn, a = 2 π - arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn

해법을 원래 방정식에 연결하여 검증

솔루션을 에 연결하여 확인합니다

129.8 sin (a) - 0.6129.8 cos (a) = 121.79

방정식에 맞지 않는 것은 제거하십시오.

솔루션 확인

arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn :

거짓

arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn

n = 1

끼우다

arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 π 1

129.8 sin (a) - 0.6129.8 cos (a) = 121.79

위한 {\ quad}끼우다{\ quad}

a = arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 π 1

12 \cdot 9.8 sin (arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 π 1) - 0.6 \cdot 12 \cdot 9.8 cos (arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 π 1) = 12 \cdot 1.79

다듬다

109.40771 \dots = 21.48

\Rightarrow 거짓

솔루션 확인

- arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn :

참

- arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn

n = 1

끼우다

- arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 π 1

129.8 sin (a) - 0.6129.8 cos (a) = 121.79

위한 {\ quad}끼우다{\ quad}

a = - arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 π 1

12 \cdot 9.8 sin (- arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 π 1) - 0.6 \cdot 12 \cdot 9.8 cos (- arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 π 1) = 12 \cdot 1.79

다듬다

21.48 = 21.48

\Rightarrow 참

솔루션 확인

arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn :

참

arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn

n = 1

끼우다

arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 π 1

129.8 sin (a) - 0.6129.8 cos (a) = 121.79

위한 {\ quad}끼우다{\ quad}

a = arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 π 1

12 \cdot 9.8 sin (arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 π 1) - 0.6 \cdot 12 \cdot 9.8 cos (arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 π 1) = 12 \cdot 1.79

다듬다

21.48 = 21.48

\Rightarrow 참

솔루션 확인

2 π - arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn :

거짓

2 π - arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn

n = 1

끼우다

2 π - arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 π 1

129.8 sin (a) - 0.6129.8 cos (a) = 121.79

위한 {\ quad}끼우다{\ quad}

a = 2 π - arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 π 1

12 \cdot 9.8 sin (2 π - arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 π 1) - 0.6 \cdot 12 \cdot 9.8 cos (2 π - arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 π 1) = 12 \cdot 1.79

다듬다

- 129.62418 \dots = 21.48

\Rightarrow 거짓

a = - arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn, a = arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn

해를 10진수 형식으로 표시

a = - 2.75844 \dots + 2 πn, a = 0.69769 \dots + 2 πn

그래프

인기 있는 예

solvefor v,a=arctan((v^2)/(gR))

so l v e f or v, a = arctan (\frac{v ^{2}}{g R})

3sin^2(x)=4sin(x)

3 sin^{2} (x) = 4 sin (x)

2cos^2(x)-7cos(x)=0

2 cos^{2} (x) - 7 cos (x) = 0

tan (x) = tan (2 x)

2 cos (x) = \frac{1}{2}