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인기 있는 삼각법 >

cos(pi/6+x)+sin(pi/3+x)=0

해법

cos (\frac{π}{6} + x) + sin (\frac{π}{3} + x) = 0

해법

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

+1

도

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n

솔루션 단계

cos (\frac{π}{6} + x) + sin (\frac{π}{3} + x) = 0

삼각성을 사용하여 다시 쓰기

cos (\frac{π}{6} + x) + sin (\frac{π}{3} + x) = 0

삼각성을 사용하여 다시 쓰기

cos (\frac{π}{6} + x)

앵글섬식별사용:

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

= cos (\frac{π}{6}) cos (x) - sin (\frac{π}{6}) sin (x)

cos (\frac{π}{6}) cos (x) - sin (\frac{π}{6}) sin (x)

단순화하세요:

\frac{3}{2} cos (x) - \frac{1}{2} sin (x)

cos (\frac{π}{6}) cos (x) - sin (\frac{π}{6}) sin (x)

cos (\frac{π}{6})

단순화하세요:

\frac{3}{2}

cos (\frac{π}{6})

다음과 같은 사소한 아이덴티티 사용:

cos (\frac{π}{6}) = \frac{3}{2}

cos (x)

주기율표

2 πn

주기:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} 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}

= \frac{3}{2} cos (x) - sin (\frac{π}{6}) sin (x)

sin (\frac{π}{6})

단순화하세요:

\frac{1}{2}

sin (\frac{π}{6})

다음과 같은 사소한 아이덴티티 사용:

sin (\frac{π}{6}) = \frac{1}{2}

sin (x)

주기율표

2 πn

주기:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} 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{3}{2} cos (x) - \frac{1}{2} sin (x)

= \frac{3}{2} cos (x) - \frac{1}{2} sin (x)

앵글섬식별사용:

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

= sin (\frac{π}{3}) cos (x) + cos (\frac{π}{3}) sin (x)

sin (\frac{π}{3}) cos (x) + cos (\frac{π}{3}) sin (x)

단순화하세요:

\frac{3}{2} cos (x) + \frac{1}{2} sin (x)

sin (\frac{π}{3}) cos (x) + cos (\frac{π}{3}) sin (x)

sin (\frac{π}{3})

단순화하세요:

\frac{3}{2}

sin (\frac{π}{3})

다음과 같은 사소한 아이덴티티 사용:

sin (\frac{π}{3}) = \frac{3}{2}

sin (x)

주기율표

2 πn

주기:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{3}{2}

= \frac{3}{2} cos (x) + cos (\frac{π}{3}) sin (x)

cos (\frac{π}{3})

단순화하세요:

\frac{1}{2}

cos (\frac{π}{3})

다음과 같은 사소한 아이덴티티 사용:

cos (\frac{π}{3}) = \frac{1}{2}

cos (x)

주기율표

2 πn

주기:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{1}{2}

= \frac{3}{2} cos (x) + \frac{1}{2} sin (x)

= \frac{3}{2} cos (x) + \frac{1}{2} sin (x)

\frac{3}{2} cos (x) - \frac{1}{2} sin (x) + \frac{3}{2} cos (x) + \frac{1}{2} sin (x) = 0

\frac{3}{2} cos (x) - \frac{1}{2} sin (x) + \frac{3}{2} cos (x) + \frac{1}{2} sin (x)

단순화하세요:

3 cos (x)

\frac{3}{2} cos (x) - \frac{1}{2} sin (x) + \frac{3}{2} cos (x) + \frac{1}{2} sin (x)

집단적 용어

= - \frac{1}{2} sin (x) + \frac{1}{2} sin (x) + \frac{3}{2} cos (x) + \frac{3}{2} cos (x)

유사 요소 추가:

\frac{3}{2} cos (x) + \frac{3}{2} cos (x) = 3 cos (x)

\frac{3}{2} cos (x) + \frac{3}{2} cos (x)

공통 용어를 추출하다

cos (x)

= cos (x) (\frac{3}{2} + \frac{3}{2})

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

\frac{3}{2} + \frac{3}{2}

규칙 적용

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

= \frac{3 + 3}{2}

3 + 3

요인:

23

3 + 3

공통 용어를 추출하다

3

= 3 (1 + 1)

다듬다

= 23

= \frac{2 3}{2}

숫자를 나눕니다:

\frac{2}{2} = 1

= 3

= 3 cos (x)

= - \frac{1}{2} sin (x) + \frac{1}{2} sin (x) + 3 cos (x)

유사 요소 추가:

- \frac{1}{2} sin (x) + \frac{1}{2} sin (x) = 0

- \frac{1}{2} sin (x) + \frac{1}{2} sin (x)

공통 용어를 추출하다

sin (x)

= sin (x) (- \frac{1}{2} + \frac{1}{2})

- \frac{1}{2} + \frac{1}{2} = 0

- \frac{1}{2} + \frac{1}{2}

분모가 같기 때문에, 분수를 합친다:

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

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

다듬다

= 0

= 0

= 3 cos (x)

3 cos (x) = 0

3 cos (x) = 0

양쪽을 다음으로 나눕니다

3

3 cos (x) = 0

양쪽을 다음으로 나눕니다

3

\frac{3 cos ( x )}{3} = \frac{0}{3}

단순화

cos (x) = 0

cos (x) = 0

일반 솔루션

cos (x) = 0

cos (x)

주기율표

2 πn

주기:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

그래프

인기 있는 예

2.55= 1/(tan(x))

2.55 = \frac{1}{tan ( x )}

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\frac{1}{4} sin (8 x) = - \frac{1}{8}, 2 cos (8 x) = 3

sin(x)-sin(2x)=0,0<= x<2pi

sin (x) - sin (2 x) = 0, 0 \leq x < 2 π

sin(2x)=(-2sqrt(6))/7

sin (2 x) = \frac{- 2 6}{7}