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受欢迎的三角函数 >

sec^2(θ)=9

解答

sec^{2} (θ) = 9

解答

θ = 1.23095 \dots + 2 πn, θ = 2 π - 1.23095 \dots + 2 πn, θ = 1.91063 \dots + 2 πn, θ = - 1.91063 \dots + 2 πn

+1

度数

θ = 70.52877 \dots^{\circ} + 36 0^{\circ} n, θ = 289.47122 \dots^{\circ} + 36 0^{\circ} n, θ = 109.47122 \dots^{\circ} + 36 0^{\circ} n, θ = - 109.47122 \dots^{\circ} + 36 0^{\circ} n

求解步骤

sec^{2} (θ) = 9

用替代法求解

sec^{2} (θ) = 9

令

: sec (θ) = u

u^{2} = 9

u^{2} = 9 : u = 3, u = - 3

u^{2} = 9

对于

x^{2} = f (a)

解为

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

u = 9, u = - 9

9 = 3

9

因式分解数字:

9 = 3^{2}

= 3^{2}

使用根式运算法则:

n a^{n} = a

3^{2} = 3

= 3

- 9 = - 3

- 9

9 = 3

9

因式分解数字:

9 = 3^{2}

= 3^{2}

使用根式运算法则:

n a^{n} = a

3^{2} = 3

= 3

= - 3

u = 3, u = - 3

u = sec (θ)

代回

sec (θ) = 3, sec (θ) = - 3

sec (θ) = 3, sec (θ) = - 3

sec (θ) = 3 : θ = arcsec (3) + 2 πn, θ = 2 π - arcsec (3) + 2 πn

sec (θ) = 3

使用反三角函数性质

sec (θ) = 3

sec (θ) = 3

的通解

sec (x) = a \Rightarrow x = arcsec (a) + 2 πn, x = 2 π - arcsec (a) + 2 πn

θ = arcsec (3) + 2 πn, θ = 2 π - arcsec (3) + 2 πn

θ = arcsec (3) + 2 πn, θ = 2 π - arcsec (3) + 2 πn

sec (θ) = - 3 : θ = arcsec (- 3) + 2 πn, θ = - arcsec (- 3) + 2 πn

sec (θ) = - 3

使用反三角函数性质

sec (θ) = - 3

sec (θ) = - 3

的通解

sec (x) = - a \Rightarrow x = arcsec (- a) + 2 πn, x = - arcsec (- a) + 2 πn

θ = arcsec (- 3) + 2 πn, θ = - arcsec (- 3) + 2 πn

θ = arcsec (- 3) + 2 πn, θ = - arcsec (- 3) + 2 πn

合并所有解

θ = arcsec (3) + 2 πn, θ = 2 π - arcsec (3) + 2 πn, θ = arcsec (- 3) + 2 πn, θ = - arcsec (- 3) + 2 πn

以小数形式表示解

θ = 1.23095 \dots + 2 πn, θ = 2 π - 1.23095 \dots + 2 πn, θ = 1.91063 \dots + 2 πn, θ = - 1.91063 \dots + 2 πn

作图

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