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受欢迎的三角函数 >

6|tan(x)|=6

解答

6 ∣ tan (x) ∣ = 6

解答

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

+1

度数

x = 13 5^{\circ} + 18 0^{\circ} n, x = 4 5^{\circ} + 18 0^{\circ} n

求解步骤

6 ∣ tan (x) ∣ = 6

用替代法求解

6 ∣ tan (x) ∣ = 6

令

: tan (x) = u

6 ∣ u ∣ = 6

6 ∣ u ∣ = 6 : u = - 1 or u = 1

6 ∣ u ∣ = 6

两边除以

6

6 ∣ u ∣ = 6

两边除以

6

\frac{6 ∣ u ∣}{6} = \frac{6}{6}

化简

∣ u ∣ = 1

∣ u ∣ = 1

使用绝对值运算法则: 若

∣ u ∣ = a, a > 0

，则

u = a

or

u = - a

u = - 1 or u = 1

u = tan (x)

代回

tan (x) = - 1 or tan (x) = 1

tan (x) = - 1 or tan (x) = 1

tan (x) = - 1 : x = \frac{3 π}{4} + πn

tan (x) = - 1

tan (x) = - 1

的通解

tan (x)

周期表（周期为

πn

）：

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{3 π}{4} + πn

x = \frac{3 π}{4} + πn

tan (x) = 1 : x = \frac{π}{4} + πn

tan (x) = 1

tan (x) = 1

的通解

tan (x)

周期表（周期为

πn

）：

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

合并所有解

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

作图

流行的例子

7 sin (2 x) = - 2

(sin(x)+cos(x))=1

(sin (x) + cos (x)) = 1

sin(θ)=0.72437

sin (θ) = 0.72437

cos (x) = \frac{5}{12}

solvefor a,90=180-2*arccos((2a)/c)

so l v e f or a, 9 0^{\circ} = 18 0^{\circ} - 2 \cdot arccos (\frac{2 a}{c})