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인기 있는 삼각법 >

cos^2(2x)>(2sqrt(3))/4

해법

cos^{2} (2 x) > \frac{2 3}{4}

해법

- \frac{arccos ( \frac{3}{2} )}{2} + πn < x < \frac{arccos ( \frac{3}{2} )}{2} + πn or \frac{arccos ( - \frac{3}{2} )}{2} + πn < x < \frac{2 π - arccos ( - \frac{3}{2} )}{2} + πn

+2

간격 표기법

- \frac{arccos ( \frac{3}{2} )}{2} + πn, \frac{arccos ( \frac{3}{2} )}{2} + πn \cup \frac{arccos ( - \frac{3}{2} )}{2} + πn, \frac{2 π - arccos ( - \frac{3}{2} )}{2} + πn

소수

- 0.18736 \dots + πn < x < 0.18736 \dots + πn or 1.38342 \dots + πn < x < 1.75816 \dots + πn

솔루션 단계

cos^{2} (2 x) > \frac{2 3}{4}

u^{n} > a

위한,

n

균등하다 이면 그렇다면

u < - n a or u > n a

cos (2 x) < - \frac{2 3}{4} or cos (2 x) > \frac{2 3}{4}

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

\frac{2 3}{4}

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

\frac{2 3}{4}

공통 요인 취소:

2

= \frac{3}{2}

= \frac{3}{2}

cos (2 x) < - \frac{3}{2} or cos (2 x) > \frac{3}{2}

cos (2 x) < - \frac{3}{2} : \frac{arccos ( - \frac{3}{2} )}{2} + πn < x < \frac{2 π - arccos ( - \frac{3}{2} )}{2} + πn

cos (2 x) < - \frac{3}{2}

위해서

cos (x) < a

, 이면

- 1 < a \leq 1

그렇다면

arccos (a) + 2 πn < x < 2 π - arccos (a) + 2 πn

arccos - \frac{3}{2} + 2 πn < 2 x < 2 π - arccos - \frac{3}{2} + 2 πn

만약에

a < u < b

그렇다면

a < u and u < b

arccos - \frac{3}{2} + 2 πn < 2 x and 2 x < 2 π - arccos - \frac{3}{2} + 2 πn

arccos - \frac{3}{2} + 2 πn < 2 x : x > \frac{arccos ( - \frac{3}{2} )}{2} + πn

arccos - \frac{3}{2} + 2 πn < 2 x

측면 전환

2 x > arccos - \frac{3}{2} + 2 πn

양쪽을 다음으로 나눕니다

2

2 x > arccos - \frac{3}{2} + 2 πn

양쪽을 다음으로 나눕니다

2

\frac{2 x}{2} > \frac{arccos ( - \frac{3}{2} )}{2} + \frac{2 πn}{2}

단순화

x > \frac{arccos ( - \frac{3}{2} )}{2} + πn

x > \frac{arccos ( - \frac{3}{2} )}{2} + πn

2 x < 2 π - arccos - \frac{3}{2} + 2 πn : x < \frac{2 π - arccos ( - \frac{3}{2} )}{2} + πn

2 x < 2 π - arccos - \frac{3}{2} + 2 πn

양쪽을 다음으로 나눕니다

2

2 x < 2 π - arccos - \frac{3}{2} + 2 πn

양쪽을 다음으로 나눕니다

2

\frac{2 x}{2} < \frac{2 π}{2} - \frac{arccos ( - \frac{3}{2} )}{2} + \frac{2 πn}{2}

단순화

x < π - \frac{arccos ( - \frac{3}{2} )}{2} + πn

π - \frac{arccos ( - \frac{3}{2} )}{2}

간소화하다 :

\frac{2 π - arccos ( - \frac{3}{2} )}{2}

π - \frac{arccos ( - \frac{3}{2} )}{2}

요소를 분수로 변환:

π = \frac{π 2}{2}

= \frac{π 2}{2} - \frac{arccos ( - \frac{3}{2} )}{2}

분모가 같기 때문에, 분수를 합친다:

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

= \frac{π 2 - arccos ( - \frac{3}{2} )}{2}

x < \frac{2 π - arccos ( - \frac{3}{2} )}{2} + πn

x < \frac{2 π - arccos ( - \frac{3}{2} )}{2} + πn

간격 결합

x > \frac{arccos ( - \frac{3}{2} )}{2} + πn and x < \frac{2 π - arccos ( - \frac{3}{2} )}{2} + πn

중복 구간 병합

\frac{arccos ( - \frac{3}{2} )}{2} + πn < x < \frac{2 π - arccos ( - \frac{3}{2} )}{2} + πn

cos (2 x) > \frac{3}{2} : - \frac{arccos ( \frac{3}{2} )}{2} + πn < x < \frac{arccos ( \frac{3}{2} )}{2} + πn

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

위해서

cos (x) > a

, 이면

- 1 \leq a < 1

그렇다면

- arccos (a) + 2 πn < x < arccos (a) + 2 πn

- arccos \frac{3}{2} + 2 πn < 2 x < arccos \frac{3}{2} + 2 πn

만약에

a < u < b

그렇다면

a < u and u < b

- arccos \frac{3}{2} + 2 πn < 2 x and 2 x < arccos \frac{3}{2} + 2 πn

- arccos \frac{3}{2} + 2 πn < 2 x : x > - \frac{arccos ( \frac{3}{2} )}{2} + πn

- arccos \frac{3}{2} + 2 πn < 2 x

측면 전환

2 x > - arccos \frac{3}{2} + 2 πn

양쪽을 다음으로 나눕니다

2

2 x > - arccos \frac{3}{2} + 2 πn

양쪽을 다음으로 나눕니다

2

\frac{2 x}{2} > - \frac{arccos ( \frac{3}{2} )}{2} + \frac{2 πn}{2}

단순화

x > - \frac{arccos ( \frac{3}{2} )}{2} + πn

x > - \frac{arccos ( \frac{3}{2} )}{2} + πn

2 x < arccos \frac{3}{2} + 2 πn : x < \frac{arccos ( \frac{3}{2} )}{2} + πn

2 x < arccos \frac{3}{2} + 2 πn

양쪽을 다음으로 나눕니다

2

2 x < arccos \frac{3}{2} + 2 πn

양쪽을 다음으로 나눕니다

2

\frac{2 x}{2} < \frac{arccos ( \frac{3}{2} )}{2} + \frac{2 πn}{2}

단순화

x < \frac{arccos ( \frac{3}{2} )}{2} + πn

x < \frac{arccos ( \frac{3}{2} )}{2} + πn

간격 결합

x > - \frac{arccos ( \frac{3}{2} )}{2} + πn and x < \frac{arccos ( \frac{3}{2} )}{2} + πn

중복 구간 병합

- \frac{arccos ( \frac{3}{2} )}{2} + πn < x < \frac{arccos ( \frac{3}{2} )}{2} + πn

간격 결합

\frac{arccos ( - \frac{3}{2} )}{2} + πn < x < \frac{2 π - arccos ( - \frac{3}{2} )}{2} + πn or - \frac{arccos ( \frac{3}{2} )}{2} + πn < x < \frac{arccos ( \frac{3}{2} )}{2} + πn

중복 구간 병합

- \frac{arccos ( \frac{3}{2} )}{2} + πn < x < \frac{arccos ( \frac{3}{2} )}{2} + πn or \frac{arccos ( - \frac{3}{2} )}{2} + πn < x < \frac{2 π - arccos ( - \frac{3}{2} )}{2} + πn

인기 있는 예

cos (y) > 0

4 cos (2 x - 30) > 0

sin (a) > 1

cos (x - y) > 0

4sin(x)cos(x)+1<= 0

4 sin (x) cos (x) + 1 \leq 0