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受欢迎的三角函数 >

tan^2(θ)-4=0

解答

tan^{2} (θ) - 4 = 0

解答

θ = 1.10714 \dots + πn, θ = - 1.10714 \dots + πn

+1

度数

θ = 63.43494 \dots^{\circ} + 18 0^{\circ} n, θ = - 63.43494 \dots^{\circ} + 18 0^{\circ} n

求解步骤

tan^{2} (θ) - 4 = 0

用替代法求解

tan^{2} (θ) - 4 = 0

令

: tan (θ) = u

u^{2} - 4 = 0

u^{2} - 4 = 0 : u = 2, u = - 2

u^{2} - 4 = 0

将

4

到右边

u^{2} - 4 = 0

两边加上

4

u^{2} - 4 + 4 = 0 + 4

化简

u^{2} = 4

u^{2} = 4

对于

x^{2} = f (a)

解为

x = f (a), - f (a)

u = 4, u = - 4

4 = 2

4

因式分解数字:

4 = 2^{2}

= 2^{2}

使用根式运算法则:

n a^{n} = a

2^{2} = 2

= 2

- 4 = - 2

- 4

4 = 2

4

因式分解数字:

4 = 2^{2}

= 2^{2}

使用根式运算法则:

n a^{n} = a

2^{2} = 2

= 2

= - 2

u = 2, u = - 2

u = tan (θ)

代回

tan (θ) = 2, tan (θ) = - 2

tan (θ) = 2, tan (θ) = - 2

tan (θ) = 2 : θ = arctan (2) + πn

tan (θ) = 2

使用反三角函数性质

tan (θ) = 2

tan (θ) = 2

的通解

tan (x) = a \Rightarrow x = arctan (a) + πn

θ = arctan (2) + πn

θ = arctan (2) + πn

tan (θ) = - 2 : θ = arctan (- 2) + πn

tan (θ) = - 2

使用反三角函数性质

tan (θ) = - 2

tan (θ) = - 2

的通解

tan (x) = - a \Rightarrow x = arctan (- a) + πn

θ = arctan (- 2) + πn

θ = arctan (- 2) + πn

合并所有解

θ = arctan (2) + πn, θ = arctan (- 2) + πn

以小数形式表示解

θ = 1.10714 \dots + πn, θ = - 1.10714 \dots + πn

作图

流行的例子

csc^2(θ)-2csc(θ)-8=0

csc^{2} (θ) - 2 csc (θ) - 8 = 0

(tan(θ)+1)(cos(θ)+1)=0

(tan (θ) + 1) (cos (θ) + 1) = 0

sec (θ) = \frac{5}{3}

1-cos(x)=sqrt(3)sin(x)

1 - cos (x) = 3 sin (x)

sin (θ) = \frac{7}{25}