tan(x)<=-2sqrt(3)

解答

tan (x) \leq - 23

- \frac{π}{2} + πn < x \leq - arctan (23) + πn

间隔符号

(- \frac{π}{2} + πn, - arctan (23) + πn]

十进制

- 1.57079 \dots + πn < x \leq - 1.28976 \dots + πn

求解步骤

tan (x) \leq - 23

若

tan (x) \leq a

，则

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

- \frac{π}{2} + πn < x \leq arctan (- 23) + πn

化简

arctan (- 23) : - arctan (23)

arctan (- 23)

利用以下特性:

arctan (- x) = - arctan (x)

arctan (- 23) = - arctan (23)

= - arctan (23)

- \frac{π}{2} + πn < x \leq - arctan (23) + πn

tan (x) \leq 1, 0 \leq x \leq 2 π

(sin (x)) < \frac{1}{2}

\frac{2 cos ( x ) - 2}{sin ( 2 x )} \leq 0

\frac{( 4 \cdot cos ^{2} ( x ) - 3 )}{( sin ( x ) + cos ( x ) + 5 )} < 0

\frac{1}{2} \leq sin (x), cos (x) \leq \frac{2}{2}