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受欢迎的三角函数 >

12tan(x)+5=5tan(x)+5

解答

12 tan (x) + 5 = 5 tan (x) + 5

解答

x = πn

+1

度数

x = 0^{\circ} + 18 0^{\circ} n

求解步骤

12 tan (x) + 5 = 5 tan (x) + 5

用替代法求解

12 tan (x) + 5 = 5 tan (x) + 5

令

: tan (x) = u

12 u + 5 = 5 u + 5

12 u + 5 = 5 u + 5 : u = 0

12 u + 5 = 5 u + 5

两边减去

5

12 u + 5 - 5 = 5 u + 5 - 5

化简

12 u = 5 u

将

5 u

para o lado esquerdo

12 u = 5 u

两边减去

5 u

12 u - 5 u = 5 u - 5 u

化简

7 u = 0

7 u = 0

两边除以

7

7 u = 0

两边除以

7

\frac{7 u}{7} = \frac{0}{7}

化简

u = 0

u = 0

u = tan (x)

代回

tan (x) = 0

tan (x) = 0

tan (x) = 0 : x = πn

tan (x) = 0

tan (x) = 0

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 = 0 + πn

x = 0 + πn

解

x = 0 + πn : x = πn

x = 0 + πn

0 + πn = πn

x = πn

x = πn

合并所有解

x = πn

作图

流行的例子

4cos(x)+3sin(x)=0

4 cos (x) + 3 sin (x) = 0

5cos(θ)=-5sin(-θ)

5 cos (θ) = - 5 sin (- θ)

cos(x)-2sin(x)cos(x)=0,0<= x<= 2pi

cos (x) - 2 sin (x) cos (x) = 0, 0 \leq x \leq 2 π

sec^2(x)+6tan(x)=8

sec^{2} (x) + 6 tan (x) = 8

tan (θ) = - \frac{3}{8}