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受欢迎的三角函数 >

sec^2(θ)-25=0

解答

sec^{2} (θ) - 25 = 0

解答

θ = 1.36943 \dots + 2 πn, θ = 2 π - 1.36943 \dots + 2 πn, θ = 1.77215 \dots + 2 πn, θ = - 1.77215 \dots + 2 πn

+1

度数

θ = 78.46304 \dots^{\circ} + 36 0^{\circ} n, θ = 281.53695 \dots^{\circ} + 36 0^{\circ} n, θ = 101.53695 \dots^{\circ} + 36 0^{\circ} n, θ = - 101.53695 \dots^{\circ} + 36 0^{\circ} n

求解步骤

sec^{2} (θ) - 25 = 0

用替代法求解

sec^{2} (θ) - 25 = 0

令

: sec (θ) = u

u^{2} - 25 = 0

u^{2} - 25 = 0 : u = 5, u = - 5

u^{2} - 25 = 0

将

25

到右边

u^{2} - 25 = 0

两边加上

25

u^{2} - 25 + 25 = 0 + 25

化简

u^{2} = 25

u^{2} = 25

对于

x^{2} = f (a)

解为

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

u = 25, u = - 25

25 = 5

25

因式分解数字:

25 = 5^{2}

= 5^{2}

使用根式运算法则:

n a^{n} = a

5^{2} = 5

= 5

- 25 = - 5

- 25

25 = 5

25

因式分解数字:

25 = 5^{2}

= 5^{2}

使用根式运算法则:

n a^{n} = a

5^{2} = 5

= 5

= - 5

u = 5, u = - 5

u = sec (θ)

代回

sec (θ) = 5, sec (θ) = - 5

sec (θ) = 5, sec (θ) = - 5

sec (θ) = 5 : θ = arcsec (5) + 2 πn, θ = 2 π - arcsec (5) + 2 πn

sec (θ) = 5

使用反三角函数性质

sec (θ) = 5

sec (θ) = 5

的通解

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

θ = arcsec (5) + 2 πn, θ = 2 π - arcsec (5) + 2 πn

θ = arcsec (5) + 2 πn, θ = 2 π - arcsec (5) + 2 πn

sec (θ) = - 5 : θ = arcsec (- 5) + 2 πn, θ = - arcsec (- 5) + 2 πn

sec (θ) = - 5

使用反三角函数性质

sec (θ) = - 5

sec (θ) = - 5

的通解

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

θ = arcsec (- 5) + 2 πn, θ = - arcsec (- 5) + 2 πn

θ = arcsec (- 5) + 2 πn, θ = - arcsec (- 5) + 2 πn

合并所有解

θ = arcsec (5) + 2 πn, θ = 2 π - arcsec (5) + 2 πn, θ = arcsec (- 5) + 2 πn, θ = - arcsec (- 5) + 2 πn

以小数形式表示解

θ = 1.36943 \dots + 2 πn, θ = 2 π - 1.36943 \dots + 2 πn, θ = 1.77215 \dots + 2 πn, θ = - 1.77215 \dots + 2 πn

作图

流行的例子

cos (6 x) = - 1

cos(a)=-(sqrt(3))/2

cos (a) = - \frac{3}{2}

8sin(2x)=8cos(x)

8 sin (2 x) = 8 cos (x)

cos(t)=(sqrt(2))/2

cos (t) = \frac{2}{2}

tan^2(θ)+5tan(θ)+6=0

tan^{2} (θ) + 5 tan (θ) + 6 = 0