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受欢迎的三角函数 >

4sqrt(2)tan(x)-sqrt(2)=3sqrt(2)tan(x)

解答

42 tan (x) - 2 = 32 tan (x)

解答

x = \frac{π}{4} + πn

+1

度数

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

求解步骤

42 tan (x) - 2 = 32 tan (x)

用替代法求解

42 tan (x) - 2 = 32 tan (x)

令

: tan (x) = u

42 u - 2 = 32 u

42 u - 2 = 32 u : u = 1

42 u - 2 = 32 u

将

2

到右边

42 u - 2 = 32 u

两边加上

2

42 u - 2 + 2 = 32 u + 2

化简

42 u = 32 u + 2

42 u = 32 u + 2

将

32 u

para o lado esquerdo

42 u = 32 u + 2

两边减去

32 u

42 u - 32 u = 32 u + 2 - 32 u

化简

42 u - 32 u = 32 u + 2 - 32 u

化简

42 u - 32 u : 2 u

42 u - 32 u

同类项相加:

42 u - 32 u = 2 u

= 2 u

化简

32 u + 2 - 32 u : 2

32 u + 2 - 32 u

同类项相加:

32 u - 32 u = 0

= 2

2 u = 2

2 u = 2

2 u = 2

两边除以

2

2 u = 2

两边除以

2

\frac{2 u}{2} = \frac{2}{2}

化简

u = 1

u = 1

u = tan (x)

代回

tan (x) = 1

tan (x) = 1

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{π}{4} + πn

作图

流行的例子

7sin(2x)+12cos(x)=0

7 sin (2 x) + 12 cos (x) = 0

solvefor θ,cos(θ)=-cos(40)

so l v e f or θ, cos (θ) = - cos (4 0^{\circ})

7sin(B)+3=sin(B)+2

7 sin (B) + 3 = sin (B) + 2

4 cos (x) = 3

cos(x+1/6 pi)cos(x-1/6 pi)=cos(2x)

cos (x + \frac{1}{6} π) cos (x - \frac{1}{6} π) = cos (2 x)