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인기 있는 삼각법 >

14cos(x^2)sin(e^x)=0

해법

14 cos (x^{2}) sin (e^{x}) = 0

해법

x = \frac{π + 4 πn}{2}, x = - \frac{π + 4 πn}{2}, x = \frac{3 π + 4 πn}{2}, x = - \frac{3 π + 4 πn}{2}, x = ln (2 πn), x = ln (π + 2 πn)

+1

도

x = 0^{\circ} + 160.57117 \dots^{\circ} n, x = 0^{\circ} - 160.57117 \dots^{\circ} n, x = 0^{\circ} + 189.99037 \dots^{\circ} n, x = 0^{\circ} - 189.99037 \dots^{\circ} n, x = 0^{\circ} + 105.30259 \dots^{\circ} n, x = 0^{\circ} + 128.53403 \dots^{\circ} n

솔루션 단계

14 cos (x^{2}) sin (e^{x}) = 0

각 부분을 개별적으로 해결

cos (x^{2}) = 0 or sin (e^{x}) = 0

cos (x^{2}) = 0 : x = \frac{π + 4 πn}{2}, x = - \frac{π + 4 πn}{2}, x = \frac{3 π + 4 πn}{2}, x = - \frac{3 π + 4 πn}{2}

cos (x^{2}) = 0

일반 솔루션

cos (x^{2}) = 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^{2} = \frac{π}{2} + 2 πn, x^{2} = \frac{3 π}{2} + 2 πn

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

x^{2} = \frac{π}{2} + 2 πn

해결 :

x = \frac{π + 4 πn}{2}, x = - \frac{π + 4 πn}{2}

x^{2} = \frac{π}{2} + 2 πn

위해서

x^{2} = f (a)

해결책은

x = f (a), - f (a)

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

\frac{π}{2} + 2 πn

단순화하세요:

\frac{π + 4 πn}{2}

\frac{π}{2} + 2 πn

\frac{π}{2} + 2 πn

합류하다:

\frac{π + 4 πn}{2}

\frac{π}{2} + 2 πn

요소를 분수로 변환:

2 πn = \frac{2 πn 2}{2}

= \frac{π}{2} + \frac{2 πn \cdot 2}{2}

분모가 같기 때문에, 분수를 합친다:

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

= \frac{π + 2 πn \cdot 2}{2}

숫자를 곱하시오:

2 \cdot 2 = 4

= \frac{π + 4 πn}{2}

= \frac{π + 4 πn}{2}

- \frac{π}{2} + 2 πn

단순화하세요:

- \frac{π + 4 πn}{2}

- \frac{π}{2} + 2 πn

\frac{π}{2} + 2 πn

합류하다:

\frac{π + 4 πn}{2}

\frac{π}{2} + 2 πn

요소를 분수로 변환:

2 πn = \frac{2 πn 2}{2}

= \frac{π}{2} + \frac{2 πn \cdot 2}{2}

분모가 같기 때문에, 분수를 합친다:

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

= \frac{π + 2 πn \cdot 2}{2}

숫자를 곱하시오:

2 \cdot 2 = 4

= \frac{π + 4 πn}{2}

= - \frac{π + 4 πn}{2}

x = \frac{π + 4 πn}{2}, x = - \frac{π + 4 πn}{2}

x^{2} = \frac{3 π}{2} + 2 πn

해결 :

x = \frac{3 π + 4 πn}{2}, x = - \frac{3 π + 4 πn}{2}

x^{2} = \frac{3 π}{2} + 2 πn

위해서

x^{2} = f (a)

해결책은

x = f (a), - f (a)

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

\frac{3 π}{2} + 2 πn

단순화하세요:

\frac{3 π + 4 πn}{2}

\frac{3 π}{2} + 2 πn

\frac{3 π}{2} + 2 πn

합류하다:

\frac{3 π + 4 πn}{2}

\frac{3 π}{2} + 2 πn

요소를 분수로 변환:

2 πn = \frac{2 πn 2}{2}

= \frac{3 π}{2} + \frac{2 πn \cdot 2}{2}

분모가 같기 때문에, 분수를 합친다:

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

= \frac{3 π + 2 πn \cdot 2}{2}

숫자를 곱하시오:

2 \cdot 2 = 4

= \frac{3 π + 4 πn}{2}

= \frac{3 π + 4 πn}{2}

- \frac{3 π}{2} + 2 πn

단순화하세요:

- \frac{3 π + 4 πn}{2}

- \frac{3 π}{2} + 2 πn

\frac{3 π}{2} + 2 πn

합류하다:

\frac{3 π + 4 πn}{2}

\frac{3 π}{2} + 2 πn

요소를 분수로 변환:

2 πn = \frac{2 πn 2}{2}

= \frac{3 π}{2} + \frac{2 πn \cdot 2}{2}

분모가 같기 때문에, 분수를 합친다:

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

= \frac{3 π + 2 πn \cdot 2}{2}

숫자를 곱하시오:

2 \cdot 2 = 4

= \frac{3 π + 4 πn}{2}

= - \frac{3 π + 4 πn}{2}

x = \frac{3 π + 4 πn}{2}, x = - \frac{3 π + 4 πn}{2}

x = \frac{π + 4 πn}{2}, x = - \frac{π + 4 πn}{2}, x = \frac{3 π + 4 πn}{2}, x = - \frac{3 π + 4 πn}{2}

sin (e^{x}) = 0 : x = ln (2 πn), x = ln (π + 2 πn)

sin (e^{x}) = 0

일반 솔루션

sin (e^{x}) = 0

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}

e^{x} = 0 + 2 πn, e^{x} = π + 2 πn

e^{x} = 0 + 2 πn, e^{x} = π + 2 πn

e^{x} = 0 + 2 πn

해결 :

x = ln (2 πn)

e^{x} = 0 + 2 πn

지수 규칙 적용

e^{x} = 0 + 2 πn

만약에

f (x) = g (x)

, 그렇다면

ln (f (x)) = ln (g (x))

ln (e^{x}) = ln (0 + 2 πn)

로그 규칙 적용:

ln (e^{a}) = a

ln (e^{x}) = x

x = ln (0 + 2 πn)

단순화

x = ln (2 πn)

x = ln (2 πn)

e^{x} = π + 2 πn

해결 :

x = ln (π + 2 πn)

e^{x} = π + 2 πn

지수 규칙 적용

e^{x} = π + 2 πn

만약에

f (x) = g (x)

, 그렇다면

ln (f (x)) = ln (g (x))

ln (e^{x}) = ln (π + 2 πn)

로그 규칙 적용:

ln (e^{a}) = a

ln (e^{x}) = x

x = ln (π + 2 πn)

x = ln (π + 2 πn)

x = ln (2 πn), x = ln (π + 2 πn)

모든 솔루션 결합

x = \frac{π + 4 πn}{2}, x = - \frac{π + 4 πn}{2}, x = \frac{3 π + 4 πn}{2}, x = - \frac{3 π + 4 πn}{2}, x = ln (2 πn), x = ln (π + 2 πn)

그래프

인기 있는 예

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