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受欢迎的三角函数 >

tan^2(θ)-16=0

解答

tan^{2} (θ) - 16 = 0

解答

θ = 1.32581 \dots + πn, θ = - 1.32581 \dots + πn

+1

度数

θ = 75.96375 \dots^{\circ} + 18 0^{\circ} n, θ = - 75.96375 \dots^{\circ} + 18 0^{\circ} n

求解步骤

tan^{2} (θ) - 16 = 0

用替代法求解

tan^{2} (θ) - 16 = 0

令

: tan (θ) = u

u^{2} - 16 = 0

u^{2} - 16 = 0 : u = 4, u = - 4

u^{2} - 16 = 0

将

16

到右边

u^{2} - 16 = 0

两边加上

16

u^{2} - 16 + 16 = 0 + 16

化简

u^{2} = 16

u^{2} = 16

对于

x^{2} = f (a)

解为

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

u = 16, u = - 16

16 = 4

16

因式分解数字:

16 = 4^{2}

= 4^{2}

使用根式运算法则:

n a^{n} = a

4^{2} = 4

= 4

- 16 = - 4

- 16

16 = 4

16

因式分解数字:

16 = 4^{2}

= 4^{2}

使用根式运算法则:

n a^{n} = a

4^{2} = 4

= 4

= - 4

u = 4, u = - 4

u = tan (θ)

代回

tan (θ) = 4, tan (θ) = - 4

tan (θ) = 4, tan (θ) = - 4

tan (θ) = 4 : θ = arctan (4) + πn

tan (θ) = 4

使用反三角函数性质

tan (θ) = 4

tan (θ) = 4

的通解

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

θ = arctan (4) + πn

θ = arctan (4) + πn

tan (θ) = - 4 : θ = arctan (- 4) + πn

tan (θ) = - 4

使用反三角函数性质

tan (θ) = - 4

tan (θ) = - 4

的通解

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

θ = arctan (- 4) + πn

θ = arctan (- 4) + πn

合并所有解

θ = arctan (4) + πn, θ = arctan (- 4) + πn

以小数形式表示解

θ = 1.32581 \dots + πn, θ = - 1.32581 \dots + πn

作图

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