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인기 있는 삼각법 >

tan(2x)<= 1/3 sqrt(3),pi<= x<= (3pi)/2

해법

tan (2 x) \leq \frac{1}{3} 3, π \leq x \leq \frac{3 π}{2}

해법

π \leq x \leq π + \frac{π}{12} or \frac{5 π}{4} < x \leq \frac{3 π}{2}

+2

간격 표기법

[π, π + \frac{π}{12}] \cup (\frac{5 π}{4}, \frac{3 π}{2}]

소수

3.14159 \dots \leq x \leq 3.40339 \dots or 3.92699 \dots < x \leq 4.71238 \dots

솔루션 단계

tan (2 x) \leq \frac{1}{3} 3, π \leq x \leq \frac{3 π}{2}

\frac{1}{3} 3

간소화하다 :

\frac{3}{3}

\frac{1}{3} 3

다중 분수:

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

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

곱하다:

1 \cdot 3 = 3

= \frac{3}{3}

만약에

tan (x) \leq a

그렇다면

- \frac{π}{2} + πn < x \leq arctan (a) + πn

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

만약에

a < u \leq b

그렇다면

a < u and u \leq b

- \frac{π}{2} + πn < 2 x and 2 x \leq arctan (\frac{3}{3}) + πn

- \frac{π}{2} + πn < 2 x : x > - \frac{π}{4} + \frac{πn}{2}

- \frac{π}{2} + πn < 2 x

측면 전환

2 x > - \frac{π}{2} + πn

양쪽을 다음으로 나눕니다

2

2 x > - \frac{π}{2} + πn

양쪽을 다음으로 나눕니다

2

\frac{2 x}{2} > - \frac{\frac{π}{2}}{2} + \frac{πn}{2}

단순화

\frac{2 x}{2} > - \frac{\frac{π}{2}}{2} + \frac{πn}{2}

\frac{2 x}{2}

간소화하다 :

x

\frac{2 x}{2}

숫자를 나눕니다:

\frac{2}{2} = 1

= x

- \frac{\frac{π}{2}}{2} + \frac{πn}{2}

간소화하다 :

- \frac{π}{4} + \frac{πn}{2}

- \frac{\frac{π}{2}}{2} + \frac{πn}{2}

\frac{\frac{π}{2}}{2} = \frac{π}{4}

\frac{\frac{π}{2}}{2}

분수 규칙 적용:

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

= \frac{π}{2 \cdot 2}

숫자를 곱하시오:

2 \cdot 2 = 4

= \frac{π}{4}

= - \frac{π}{4} + \frac{πn}{2}

x > - \frac{π}{4} + \frac{πn}{2}

x > - \frac{π}{4} + \frac{πn}{2}

x > - \frac{π}{4} + \frac{πn}{2}

2 x \leq arctan (\frac{3}{3}) + πn : x \leq \frac{π}{12} + \frac{πn}{2}

2 x \leq arctan (\frac{3}{3}) + πn

arctan (\frac{3}{3}) + πn

간소화하다 :

\frac{π}{6} + πn

arctan (\frac{3}{3}) + πn

다음과 같은 사소한 아이덴티티 사용:

arctan (\frac{3}{3}) = \frac{π}{6}

x 0 \frac{3}{3} 13 arctan (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} arctan (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ}

= \frac{π}{6} + πn

2 x \leq \frac{π}{6} + πn

양쪽을 다음으로 나눕니다

2

2 x \leq \frac{π}{6} + πn

양쪽을 다음으로 나눕니다

2

\frac{2 x}{2} \leq \frac{\frac{π}{6}}{2} + \frac{πn}{2}

단순화

\frac{2 x}{2} \leq \frac{\frac{π}{6}}{2} + \frac{πn}{2}

\frac{2 x}{2}

간소화하다 :

x

\frac{2 x}{2}

숫자를 나눕니다:

\frac{2}{2} = 1

= x

\frac{\frac{π}{6}}{2} + \frac{πn}{2}

간소화하다 :

\frac{π}{12} + \frac{πn}{2}

\frac{\frac{π}{6}}{2} + \frac{πn}{2}

\frac{\frac{π}{6}}{2} = \frac{π}{12}

\frac{\frac{π}{6}}{2}

분수 규칙 적용:

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

= \frac{π}{6 \cdot 2}

숫자를 곱하시오:

6 \cdot 2 = 12

= \frac{π}{12}

= \frac{π}{12} + \frac{πn}{2}

x \leq \frac{π}{12} + \frac{πn}{2}

x \leq \frac{π}{12} + \frac{πn}{2}

x \leq \frac{π}{12} + \frac{πn}{2}

간격 결합

x > - \frac{π}{4} + \frac{πn}{2} and x \leq \frac{π}{12} + \frac{πn}{2}

중복 구간 병합

- \frac{π}{4} + \frac{π}{2} n < x \leq \frac{π}{12} + \frac{π}{2} n

간격 결합

- \frac{π}{4} + \frac{π}{2} n < x \leq \frac{π}{12} + \frac{π}{2} n and π \leq x \leq \frac{3 π}{2}

π \leq x \leq π + \frac{π}{12} or \frac{5 π}{4} < x \leq \frac{3 π}{2}

그래프

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